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PRACTICAL  PHYSICS 


THE  MACMILLAN  COMPANY 

NSW  YORK   •    BOSTON   •    CHICAGO   •    DALLAS 
ATLANTA  •    SAN   FRANCISCO 

MACMILLAN  &  CO.,  LIMITED 

LONDON   •    BOMBAY   •    CALCUTTA 
MELBOURNE 

THE  MACMILLAN  CO.  OF  CANADA,  LTIX 

TORONTO 


GALILEO  GALILEI.  Born  1564,  in  Pisa,  Italy.  Died  1642.  Often  called 
"  the  father  of  modern  science  "  because  he  was  one  of  the  first  who 
thought  it  worth  while  to  subject  his  ideas  to  the  test  of  experiment. 


PRACTICAL    PHYSICS 


FUNDAMENTAL    PRINCIPLES    AND 
APPLICATIONS    TO    DAILY    LIFE 


BY 
N.  HENRY  BLACK,  A.M. 

SCIENCE    MASTER,    ROXBURY    LATIN    SCHOOL 
BOSTON,    MASS. 

AND 

HARVEY  N.  DAVIS,  PH.D. 


ASSISTANT    PROFESSOR    OF    PHYSICS 
HARVARD    UNIVERSITY 


Neto  gork 
THE   MACMILLAN   COMPANY 

1917 

All  rights  reserved 


COPYBIGHT,    1918, 

BY   THE   MACMILLAN   COMPANY. 


Set  up  and  electrotyped.     Published  June,  1913.     Reprinted 
August,  1913;  April, June,  1914;  January,  July, December,  1915; 
July,  1916;  May,  August,  1917. 


J.  8.  Cushing  Co.  —  Berwick  &  Smith  Co, 
Norwood,  Mass.,  U.S.A. 


G(  C  I  3-- 


PREFACE 

THE  most  difficult  problem  which  confronts  any  author  of 
a  textbook  is  the  selection  of  material.  This  is  usually  a 
process  of  exclusion.  One  has  always  to  keep  in  mind  the 
capacities  and  limitations,  the  interests  and  inclinations,  of 
the  young  people  most  directly  concerned,  as  well  as  the 
beauty  and  vast  extent  of  the  subject  to  be  taught.  This  is 
especially  true  of  a  first  course  in  physics.  The  number  of 
suitable  topics  is  far  greater  than  can  be  well  handled  in  any 
one-year  course,  however  substantial  it  may  be.  A  good 
book  may,  therefore,  be  judged  as  well  by  its  omissions  as  in 
any  other  way.  In  preparing  this  book,  we  have  tried  to 
select  only  those  topics  which  are  of  vital  interest  to  young 
people,  whether  or  not  they  intend  to  continue  the  study  of 
physics  in  a  college  course. 

In  particular,  we  believe  that  the  chief  value  of  the  infor- 
mational side  of  such  a  course  lies  in  its  applications  to  the 
machinery  of  daily  life.  Everybody  needs  to  know  some- 
thing about  the  working  of  electrical  machinery,  optical 
instruments,  ships,  automobiles,  and  all  those  labor-saving 
devices,  such  as  vacuum  cleaners,  fireless  cookers,  pressure 
cookers,  and  electric  irons,  which  are  found  in  many  modern 
homes.  We  have,  therefore,  drawn  as  much  of  our  illus- 
trative material  as  possible  from  the  common  devices  in 
modern  life.  We  see  no  reason  why  this  should  detract  in 
the  least  from  the  educational  value  of  the  study  of  physics, 
for  one  can  learn  to  think  straight  just  as  well  by  thinking 
about  an  electrical  generator,  as  by  thinking  about  a  Geissler 

tube. 

v 


VI  PREFACE 

This  does  not  mean  that  we  have  tried  to  make  the  sub- 
ject interesting  by  selecting  only  the  easy  topics.  There  are 
many  parts  of  physics  which  are  of  great  practical  value,  but 
are  essentially  difficult.  We  have  tried  to  present  these 
subjects  very  slowly  and  carefully,  believing  that  if  any 
presentation  is  so  simple  and  direct  that  the  student  can 
understand  it  clearly,  his  very  understanding  begets  at  once 
the  interest  which  is  fundamental. 

Even  after  a  careful  exclusion  of  material,  we  have  selected 
somewhat  more  than  it  is  probably  advisable  for  any  class  to 
undertake  in  a  single  year.  This  gives  the  teacher  an  oppor- 
tunity to  adapt  his  instruction  to  the  local  needs  of  his  com- 
munity and  to  the  amount  of  time  available.  In  particular, 
the  chapter  on  the  strength  of  materials,  the  discussion  of 
momentum,  the  chapter  on  the  beginnings  of  electricity,  the 
chapter  on  alternating  currents,  the  chapter  on  electric  waves 
and  X-rays,  and  even  the  chapter  on  sound,  may  well  be 
omitted  altogether,  or  assigned  for  outside  reading  without 
careful  discussion,  if  it  seems  desirable.  We  believe  that  it 
is  most  important  for  teachers  to  select  carefully  just  what 
material  they  can  best  use,  and  to  teach  that  thoroughly, 
rather  than  try  to  touch  upon  many  topics  superficially. 

We  think  it  of  great  importance  that  the  topics  in  a  course 
in  physics  should  be  arranged  in  the  most  teachable  order ; 
that  is,  with  the  easiest  and  simplest  topics  first.  Thus  in 
mechanics,  the  subject  of  acceleration  and  Newton's  laws  is 
essentially  hard,  and  so  we  have  put  it  at  the  end  of  that 
part  of  the  book.  On  the  other  hand,  the  simple  machines, 
such  as  the  lever  and  the  wheel  and  axle,  are  essentially 
easy,  and  so  they  come  first. 

To  understand  any  machine  clearly,  the  student  must 
have  clearly  in  mind  the  fundamental  principles  involved. 
Therefore,  although  we  have  tried  to  begin  each  new  topic, 
however  short,  with  some  concrete  illustration  familiar  to 
young  people,  we  have  proceeded,  as  rapidly  as  seemed  wise, 


PREFACE  Vll 

to  a  deduction  of  the  general  principle.  Then,  to  show  how 
to  make  use  of  this  principle,  we  have  discussed  other  prac- 
tical applications.  We  have  tried  to  emphasize  still  further 
the  value  of  principles,  that  is,  generalizations,  in  science,  by 
summarizing  at  the  end  of  each  chapter  the  principles  dis- 
cussed in  that  chapter.  In  these  summaries  we  have  aimed 
to  make  the  phrasing  brief  and  vivid  so  that  it  may  be 
easily  remembered  and  easily  used. 

The  problems  are  the  result  of  considerable  experience  in 
trying  to  find  suitable  numerical  exercises  which  will  empha- 
size and  illustrate  the  principles  involved,  with  a  minimum 
of  arithmetical  drudgery.  They,  too,  are  arranged,  within 
each  group,  as  far  as  possible  in  the  order  of  their  difficulty. 
It  should  always  be  emphasized,  however,  that  the  study  of 
physics  does  not  begin  and  end  in  the  classroom,  but  is  inti- 
mately connected  with  industrial  and  domestic  life.  It  is 
very  desirable  to  stimulate  in  students  thought  and  imagina- 
tion about  what  they  see,  and  to  get  them  into  the  habit  of 
asking  intelligent  questions  of  the  mechanics,  artisans,  and 
engineers  whom  they  meet.  We  have,  therefore,  added  at 
the  end  of  each  of  the  earlier  chapters,  and  in  many  places  in 
the  later  chapters,  questions,  which  require  some  knowledge 
gained  in  this  way  from  outside  life.  We  do  not  expect 
that  every  student  can  answer  even  a  majority  of  these  ques- 
tions at  first ;  but  after  he  has  tried  to  answer  them,  he  is  in 
a  position  to  learn  a  great  deal  from  the  subsequent  discussion 
of  them  in  the  classroom. 

Our  treatment  of  acceleration,  Newton's  laws,  kinetic  en- 
ergy and  momentum,  is  essentially  different  from  either  the 
dyne  and  poundal  method  common  in  physics  textbooks,  or 
the  "  slug  "  or  "  wog  "  method  of  engineers,  and  is  apparently 
new.  It  has,  however,  been  thoroughly  tried  out  in  the 
classroom,  and  we  find  it  simpler  and  more  direct  than  the 
usual  presentation.  We  feel  sure  that  it  is  as  precise  and 
scientific  in  its  logic  as  any  other.  It  was  first  developed  by 


Vill  PREFACE 

Professor  E.  V.  Huntington,  of  Harvard  University,  to  whom 
we  gladly  make  acknowledgment  of  priority. 

We  have  borrowed  ideas  also  from  the  books  of  Mr.  Frank 
M.  Gilley,  of  the  Chelsea  High  School,  and  Director  E. 
Grimsehl,  of  Hamburg,  Germany.  We  have  received  valu- 
able assistance  in  the  preparation  of  the  manuscript  from 
Professor  Frank  A.  Waterman,  of  Smith  College  ;  Mr.  Irving 
O.  Palmer,  of  the  Newton  Technical  High  School;  Professor 
J.  M.  Jameson  and  Professor  J.  A.  Randall,  of  Pratt  Insti- 
tute, and  many  others.  To  all  of  these  gentlemen  we  give 
our  hearty  thanks. 

We  are  indebted  to  the  General  Electric  Company,  the 
Westinghouse  Companies,  the  Columbia  Graphophone  Com- 
pany, Stone  and  Webster,  and  others  for  material  for  certain 
of  the  plates  and  illustrations. 

Finally,  we  wish  especially  to  express  our  obligation  to 
Dr.  William  C.  Collar,  lately  of  the  Roxbury  Latin  School, 
and  to  Professor  W.  S.  Franklin,  of  Lehigh  University,  but 
for  whose  initiative,  encouragement,  and  interest,  this  book 
never  would  have  been  written. 

We  shall  be  grateful  for  corrections  or  suggestions  from 
any  source. 

K  H.  B. 
H.  N.  D. 


CONTENTS 


CHAPTER 
I. 

INTRODUCTION  :  WEIGHTS  AND  MEASURES 

PAGB 

1 

II. 

SIMPLE  MACHINES      

.      13 

III. 

TV 

MECHANICS  OF  LIQUIDS     

.      47 
.      77 

XV* 

V. 

NON-PARALLEL  FORCES      ..... 

.     105 

VI. 

ELASTICITY  AND  STRENGTH  OF  MATERIALS    . 

.     120 

VII. 

ACCELERATED  MOTION      .        .        .        . 

.     133 

VIII. 
IX. 

FORCE  AND  ACCELERATION       .... 

.     146 
.     157 

X. 

HEAT  —  EXPANSION  AND  TRANSMISSION 

.     170 

XI. 

XTT 

WATER,  ICE,  AND  STEAM          .... 

.     196 
.    219 

WJ.JL* 

XIII. 
XIV. 

MAGNETISM         

.    238 

.    248 

XV. 

BATTERY  CURRENTS  

.    263 

XVI. 

MEASURING  ELECTRICITY  

.    281 

XVII. 

INDUCED  CURRENTS   

.    308 

XVIII. 

ELECTRIC  POWER        ...... 

.    318 

XIX. 

ALTERNATING  CURRENT  MACHINES 

.    358 

XX. 

SOUND          .         .        .         

.    374 

XXI. 

LAMPS  AND  REFLECTORS  

.    405 

XXII. 

LENSES  AND  OPTICAL  INSTRUMENTS 

.    427 

XXIII. 

SPECTRA  AND  COLOR         

.    456 

XXIV. 

ELECTRIC  WAVES  :  ROENTGEN  RAYS 

.    469 

PRACTICAL  PHYSICS 

CHAPTER  I 
INTRODUCTION:  WEIGHTS   AND   MEASURES 

Why  study  physics  —  content  and  divisions  of  physics  — 
physics  involves  measurement  as  well  as  merely  description 
—  units  in  English  and  metric  systems  —  density. 

1.  Why  study  physics  ?     Every  one  these  days  has  had 
something  to  do  with  machines  of  one  sort  or  another  all  his 
life.     In  the  country  we  mow,  reap,  and  thresh  grain  with 
machines ;  we  pump  water  with  windmills,  gas  or  hot-air  en- 
gines ;  and  we  skim  milk  with  a  machine  called  a  separator. 
In  the  city  we  travel  on  electric  cars ;    we  go  upstairs  on 
hydraulic  or  electric  elevators ;  we  print  our  newspapers  on 
presses  run  by  electric  motors ;  and  we  distribute  our  mail 
through  pneumatic  tubes.     In  business  and  in  commerce  we 
are  constantly  using  steam,  gas,  and  electric  engines,  cranes 
and  derricks,  locomotives,  ships,  and  automobiles,  and  per- 
haps, in  a  few  years,  we  shall  all  be  using  flying  machines. 

Every  one  has  used  some  of  these  devices  and  almost  every 
one  has  at  some  time  wondered  and  perhaps  discovered  how 
each  of  them  works.  That  is,"  almost  every  one  has  already 
begun  to  study  physics,  for  it  is  one  of  the  chief  aims  of 
physics  to  discover  all  that  can  be  known  about  such  ma- 
chines as  have  just  been  mentioned. 

2.  Physics  a  science.     The  sort  of  physics  that  will  be 
found  in  this  book  differs  from  the  sort  that  every  one  has 
been  unconsciously  studying  all  his  life,  chiefly  in  that  it 
seeks  to  answer  not  only  the  questions  "why"  and  "how," 
but  also  the  question  "how  much."      It  is  only  when  we 

B  1 


2  PRACTICAL  PHYSICS 

begin  to  measure  things  definitely  that  we  get  the  kind  oi 
information  that  helps  us  to  use  them  to  the  best  advantage. 
Thus  every  one  knows  in  a  vague  way  that  an  automobile 
goes  up  a  hill  because  the  gasolene  which  is  burned  in  the 
engine  makes  it  turn  the  driving  wheels,  and  these  in  turn 
push  against  the  road,  if  it  is  not  too  slippery,  and  thus  pro- 
pel the  automobile.  The  physicist,  when  he  had  thought  of 
all  this,  would  go  on  to  ask  himself  such  questions  as  "  How 
much  gasolene  does  it  take,  how  much  ought  it  to  take  under 
ideal  conditions,  and  what  becomes  of  the  difference?  How 
much  force  must  be  exerted  by  the  brakes  to  hold  the  auto- 
mobile on  a  hill,  how  large  a  brake  surface  will  do  this,  and 
how  strong  must  the  brake  wire  be?"  When  he  can  answer 
all  these  and  many  other  questions,  he  is  in  a  position  to  use 
his  machine  more  effectively,  and  perhaps  to  improve  its 
mechanism. 

3.  Divisions  of  physics.  The  object  of  studying  physics 
is,  then,  chiefly  to  learn  to  think  accurately  about  very 
familiar  things.  But  these  things  are  so  various  in  kind 
that  we  shall  find  it  convenient  to  divide  the  whole  subject 
into  five  divisions :  mechanics,  heat,  electricit}^  sound,  and 
light.  For  example,  suppose  we  wanted  to  make  a  thorough 
study  of  the  automobile.  Under  mechanics,  we  should  study 
about  its  cranks,  gears,  levers,  valves,  and  brakes,  including 
their  movements,  and  the  strength  of  the  material  of  their 
construction ;  under  heat,  the  engine,  its  fuel  and  radiator ; 
under  electricity,  the  spark  plug,  spark  coil,  magneto,  and 
battery ;  under  sound,  the  horns  and  trumpets ;  and  finally, 
under  light,  the  lamps  and  their  reflectors  and  lenses.  In  a 
similar  way  it  might  be  shown  that  any  piece  of  modern 
machinery,  whether  it  is  an  automobile  or  a  locomotive,  a 
motor  boat  or  an  Atlantic  liner,  a  flying  machine  or  a  sub- 
marine boat,  is  not  only  an  embodiment  of  the  principles  of 
physics,  but  has  in  very  large  measure  been  made  possible 
by  the  science  of  physics. 


INTRODUCTION:     WEIGHTS  AND  MEASURES  3 

4.  Physics   contains  some  abstractions.     While  it  is  true 
that  physics  has  to  do  chiefly  with  familiar  things,  yet  in 
order  to  make  its  study  effective  we  shall  also  have  to  considei 
some  things  which  are  not  so  familiar,  such  abstractions  as 
density  and  calories  and  wave  length  and  refraction  and 
electrical  resistance,  which  may  not  be  interesting  at  first, 
and  may  seem  to  have  little  to  do  with  our  everyday  life. 
We  shall  also  find  many  problems  to  be  solved  whose  answers 
will  seem  trivial  and  unimportant.     These  things  should  be 
done  patiently  because  they  pave  the  way  for  more  valuable 
things  later  on. 

5.  Physics  begins  with  measurements.     At  the  very  out- 
set we  may  well  recall  an  old  saying  of  Plato's :  "  If  arith- 
metic, mensuration,  and  weighing  be  taken  away  from  any 
art,  that  which  remains  will  not  be  much."     In  the  labora- 
tory the  student  will  learn  to  measure  many  different  kinds 
of  things,  not  mainly  for  the  sake  of  the  results  he  gets,  but 
rather  that  all  through  life  he  may  know  a  good  measure- 
ment when  he  sees  one,  and  may  be  able  to  discuss  accurately 
and  with  confidence  the  quantitative  problems  that  are  al- 
ways coming  up. 

6.  Units  of  measurement.     In  business  in  the  United  States 
the  value  of  things  that  are  bought  and  sold  is  measured  in 
dollars  and  cents.     Fortunately  this  system  of  money  is  made 
on  the  decimal  plan,  that  is,  in  multiples  of  ten.     Our  sys- 
tem of  weights  and  measures,  on  the  other  hand,  is  not  a 
decimal   system,   and   is   very  inconvenient.     Nevertheless,, 
since  the  pound,  foot,  quart,  gallon,  and  bushel  are  still  in 
general  use  in  Great  Britain  and  in  the  United  States,  we 
must  be  familiar  with  them.     During  the  last  century  most 
of  the  other  civilized  nations  have  adopted  the  metric  system 
of  weights  and  measures,  in  which  the  relation  of  the  units 
is  expressed  in  multiples  of  ten.     In  scientific  work  the  met- 
ric system  is  almost  universally  used  throughout  the  world, 
because  it  greatly  reduces  the  work  in  making  computations. 


4  PRACTICAL   PHYSICS 

Therefore  it  is  advisable  for  us  to  become  proficient  in  the 
use  of  both  the  English  and  the  metric  system  of  weights 
and  measures. 

7.  Meter  and  yard.     The  meter  is  the  distance  between 
two  lines  on  a  metal  bar  (Fig.  1)  which  is  preserved  in  the 

vaults  of  the  International  Bureau 
of  Weights  and  Measures  near 
Paris.* 

Since  the  length  of  this  metal 
bar  changes  a  little  with  the  tem- 
perature, the  distance  is  measured 
at  the  temperature  of  melting  ice. 
A  very  accurate  copy  of  this  bar 
FIG.  i. -The  international  is  deposited  in  the  United  States 

Bureau  of  Standards  in  Washing- 
ton, D.C.,  and  this  copy  is  the  legal  meter  of  the  United 
States. 

In  the  United  States  the  yard  is  legally  defined  as  |ffy  of 
a  meter. 

8.  Some  important  units  of  length.     In  the  problems  of 
physics    we    shall    find    that    certain    units    of    length    are 
very  frequently  used.      These  are  given  in  the  following 
table : 

UNITS  OF  LENGTH 

ENGLISH. 

1  foot  (ft.)  =  12  inches  (in.). 
1  yard  (yd.)  =  3  feet. 
1  mile  (mi.)  =  5280  feet. 


*  It  was  originally  intended  that  the  meter  should  be  equal  to  one  ten- 
millionth  part  of  the  distance  from  the  equator  to  either  pole  of  the  earth,  but 
it  is  impossible  to  reproduce  an  accurate  copy  of  the  meter  on  the  basis  of 
this  definition.  Later  measurements  have  shown  that  the  "mean  polar 
quadrant "  of  the  earth  is  about  10,002,100  meters. 


INTRODUCTION:     WEIGHTS  AND  MEASURES 

METRIC. 

1  meter  (m.)  =  1000  millimeters  (mm.). 

1  meter  =  100  centimeters  (cm.). 
1  kilometer  (km.)  =  1000  meters. 

1  inch  =  2.540  centimeters. 
1  meter  =  39.37  inches. 

CENTIMETERS 


2 


1  Square 
Jentimete 


1  Square  Inch 


INCHES  123 

FIG.  2.  — Relative  sizes  of  the  inch  and  the  centimeter. 

9.  Ijnits  of  area.     The  unit  of  area  which  is  most  exten- 
sively used  is  the  area  of  a  square  of  which  the  side  is  of  unit 
length.     Thus  the  area  of  a  city  house  lot 

is  reckoned  in  square  feet,  where  the  unit 
is  a  square  one  foot  on  each  side.  In  the 
laboratory,  area  is  often  measured  in  square 
centimeters  (cm2),  the  unit  being  a  square 
one  centimeter  on  each  side.  It  is  evident 
from  figure  3  that  one  square  inch  is  equal 
to  about  6  square  centimeters.  More  ac-  FlG; ^.-Relative sizes 

,1        • ,    •      «  r  *         r»  p  A  n.   AC  of  the  square  inch 

curately,  it  is  2.54  x  2.54,  or  6.45  square      and  the  square  ceu- 
centimeters.  timeter. 

The  usual  method  of  determining  area  is  by  calculation  from  the 
measured  linear  dimensions.-  Thus  the  area  of  a  rectangle  or  parallelo- 
gram is  equal  GO  the  base  times  the  altitude  (A  =  b  x  h).  The  area  of  a 
triangle  is  equal  to  \  the  base  times  the  altitude  (A  =  \b  x  A).  The  area 
of  a  circle  is  equal  to  3.14  times  the  square  of  the  radius  (J.  =  Tir2). 

10.  Units  of  volume  or  capacity.     The  unit  of  volume  that 
is  most  extensively  used  is  the  volume  of  a  cube  of  which  the 
edge  is  of  unit  length.     Thus  the  volume  of  a  freight  car  is 
reckoned  in  cubic  feet,  the  unit  being  a  cube  one  foot  on  each 
edge.     In  the  laboratory  we  measure  the  capacity  of  a  flask 
in  cubic  centimeters  (cm3). 


0  PRACTICAL  PHYSICS 

UNITS  OF  VOLUME 

ENGLISH. 

1  cubic  foot  (cu.  ft.)  =  1728  cubic  inches  (cu.  in.). 
1  cubic  yard  (cu.  yd.)  =  27  cubic  feet. 

1  gallon  (gal.)  =  4  quarts  (qt.)  =  231  cubic  inches 

' 

METRIC. 

1  liter  (1.)  =  1000  cubic  centimeters  (cm3) 
1  cubic  meter  (m3)  =  1000  liters. 
1  liter  =  1.06  quarts. 

The  usual  method  of  determining  the  volume  of  a  regular 
solid  is  by  calculation  from  the  measured  linear  dimensions. 
Thus  to  get  the  volume  of  a  rectangular  block  of  stone,  or  a 
box,  we  find  the  product,  length  by  width  by  depth.  In  the 
case  of  a  cylindrical  figure  we  compute  the  area  of  the  circu- 
lar base  (irr2),  and  multiply  by  the  height. 

For  measuring  liquids,  we  ordinarily  use  a  graduated  ves- 
sel of  metal  or  glass.  Thus  in  the  English  system  we  have 
gallon  and  quart  measures,  and  for  small  quantities,  fluid 
ounces  (sixteenths  of  a  pint).  In  the  metric  system,  we  have 
tfiU  in  the  laboratory  graduated  cylinders  (Fig.  4)  for  measur- 

ing liquids  in  cubic  centimeters. 
FIG.  4.  —  A 
graduated 
cylinder.  PROBLEMS 

1.  Change  2.55  meters-  to  centimeters. 

2.  Change  1575  cubic  centimeters  to  liters. 

3.  A  boy  is  5  feet  6  inches  tall.     Express  his  height  in  centimeters. 
'*•"      4.  Express  1  kilometer  as  a  decimal  part  of  a  mile. 

*•        5.   The  Falls  of  Niagara  on  the  American  side  are  about  165  feet  high. 
Express  this  in  meters.  ^ 

-6.   A  standard  size  of  automobile  tire  is  ^  inches  in  diameter  and 
fits  a-^-inch  wheel.     Express  these  dimensions  in  the  metric  system. 

7.  ^"you  wanted  to  buy  If  yards  of  silk  in  Paris,  what  length  should 
you  ask  for  ? 

8.  A  certain  type  of  Bleriot  monoplane  has  a  wing  surface  of  15 
square  meters.     Express  this  in  square  feet. 

9.  How  many  gallons  in  a  cubic  foot? 

10.   Milk  sells  in  Berlin  for  40  pfennigs  per  liter.     What  is  its  cost  in 
cents  per  quart?     (100  pfennigs  =  1  mark  =  $0.238.) 


* 

:£ 


INTRODUCTION:     WEIGHTS  AND  MEASURES 

11.  How  many  liters  does  a  tank  hold  which  is  3  meters  long,  1.5 
meters  wide,  and  1  meter  deep? 

12.  A  cylindrical  berry  box  is  measured  and  found  to  be  6.15  inches 
in  diameter  and  2.1  inches  deep.     What  is  its  capacity  in  dry  quarts? 
(In  the  United  States  it  is  understood  that  a  dry  quart  contains  67  1 
cubic  inches.) 

11.  Units  of  weight.*  The  kilogram  is  the  weight  of  a  .f  ' 
certain  platinum  -iridium  cylinder  that  is  preserved  with  the 
standard  meter  near  Paris,  or  that  of  a  very  accurate  copy  of 
this  cylinder  which  is  deposited  in  the  United  States  Bureau 
of  Standards  in  Washington.  It  was  intended  that  these 
cylinders  should  weigh  the  same  as  one  liter  of  pure  water, 
but  this  has  turned  out  to  be  not  quite  true.f  It  is,  however, 
nearly  enough  true  for  our  present  purposes.  Therefore  the 
gram,  which  is  the  one-thousandth  part  of  a  kilogram,  is  the 
weight  of  one  cubic  centimeter  of  water.  It  may  be  helpful  to  • 
remember  that  our  5-cent  nickel  piece  weighs  5  grams  and 
our  silver  half-dollar  weighs  12.5  grams. 

In  the  United   States  the  pound  avoirdupois  is  denned 


-•  *-  -- 

'*  K  tiSls.  7*trt>  tTklTS   OF   WEIGHT 

*       '* 


ENGLISH. 

1  pound  (lb.)  =  16  ounces  (oz.). 
1  ton  (T.)  =  2000  pounds. 

METRIC.  A^Z.  -2  tfi<j^-<-~* . 

1  gram  (g.)  =  1000  milligrams  (mg.). 
1  kilogram  (kg.)==  1000  grams. 

1  kilogram  =  2.20  pounds.  =    JUi-  0  f  U  J 
1  cubic  foot  of  water  weighs  62.4  pounds. 
1  cubic  centimeter  of  water  weighs  1  gram. 

*  The  distinction  between  weight  and  mass  will  be  made  in  section  148. 
t  One  liter  of  pure  water  at  4°  C.  weighs  0.999972  kilogram. 

*  .'          -  •         I       T'WM 

4     t      I  A^ 4     /     IW^t^V^L     ft^W^'    /  r;      J^   J  ^  ^1' 

M  V     V^  i 


8 


PRACTICAL  PHYSICS 


12.    Weighing  machines.     The  spring  balance  (Fig.  5)  is  a 

simple  machine  for  getting  the  weight  of  things,  or  for  meas- 
/^     uring  forces  of  other  kinds,  such  as  the  pull  exerted 
V     by  a  rope.      It  consists  of  a  coiled  spring,  and  the 
force  exerted  is  indicated  by  the  pointer  on  the  scale. 
The  spring  balance  is  very  extensively  used  because 
of  its  great  convenience,  and  its  indications  are  close 
enough  for  many  practical  purposes. 

The  platform  balance  (Fig.  6)  consists  of  a  delicately 
mounted  equal-arm  balance-beam  with  pans  supported 
at  each  end.  The  balance  is  used  to  show  the  equal- 
ity of  the  weights  of  two  bodies ;  that  is,  two  things 
are  saj^  £O  have  the  same  weight  if  they  balance  each 

other  when  supported  on  the  ends  of  an  equal-arm  balance. 

The  determination 

of    the    weight   of 

any  given  body  by 

the  platform    bal- 
ance depends  upon 

the  use  of  a  set  of 

weights,  which  may 

be  combined'  in 

such  a  way   as  to 

match  the  weight 

of  a  body. 


FIG.  5. 
Spring 
balance. 


FIG.  6.  —  Platform  balance. 


PROBLEMS 

1.  Change  755  milligrams  to  grams. 

2.  Change  1540  grams  to  kilograms. 

3.  A  girl  weighs  52.5  kilograms.     Express  her  weight  in  pounds. 

4.  American  railways  usually  allow  each  passenger  150  pounds  bag- 
gage.    Express  this  in  kilograms. 

5.  A  metric  ton  is  1000  kilograms.      How  many  pounds  is  this  in 
excess  of  the  English  ton  ? 

6.  It  is  sometimes  said,  "  A  pint  is  a  pound,  the  world  around."     How 
much  does  a  pint  of  water  weigh?     (1  quart  =  2  pints.) 


INTRODUCTION:   WEIGHTS  AND  MEASURES          9 

7.  A  bottle  is  found  to  hold  1520  grams  of  water :  (a)  how  many 
cubic  centimeters  does  it  contain  ?    (&)   how  many  liters  ? 

8.  A  boy  5  feet  4  inches  tall,  and  weighing  140  pounds,  can  walk  3.75 
miles  in  an  hour.     Express  these  facts  in  metric  units. 

13.  Density.  Every  one  knows  that  lead  is  "  heavier  "  than 
cork,  and  yet  the  question  "  which  is  heavier,  a  pound  of  lead 
or  two  pounds  of  cork  ?  "  is  foolish.  The  colloquial  word 
"  heavy  "  has  two  distinct  meanings.  Two  pounds  of  cork 
are  heavier  than  one  pound  of  lead  in  the  same  sense  that  two 
pounds  of  coal  are  heavier  than  one  pound  of  coal.  In  this 
case  the  word  "  heavy "  refers  to  the  total  weight  of  the 
material.  On  the  other  hand,  lead  is  "  heavier  "  than  cork  in 
the  sense  that  a  piece  of  lead  weighs  more  than  an  equal  bulk 
of  cork.  The  word  "  density "  is  used  to  designate  more 
precisely  this  inherent  property  of  the  lead  and  the  cork. 
That  is,  lead  has  a  greater  density  than  cork. 

The  density  of  a  substance  is  its  weight  per  unit  volume. 
Thus  the  density  of  water  is  about  62.4  pounds  per  cubic 
foot,  or  8. 34  pounds  per  gallon.  The  density  of  copper  is 
555  pounds  per  cubic  foot  or  0.321  pound  per  cubic  inch. 
In  scientific  work  it  is  usual  to  specify  the  density  of  a  sub- 
stance in  grams  per  cubic  centimeter  (g/cni3). 


TABLE  OF  DENSITIES 

Jf£^jLu/_V  «-  ^  Sram8  Per  cubic  centimeter) 

Platinum  21.5  Hard  woods  (seasoned)  0.7-1.1 

Gold  19.3  Soft  woods  (seasoned)  0.4-0.7 

Mercury  13.6  Ice  0.911 

Lead    '  11.4  Human  body  0.9-1.1 

Silver  10.5  Cork  0.25 

Copper'  8.93  Sulphuric  acid  (cone.)  1.84 

Iron  7.1-7.9  Sea  water  1.03 

Zinc  7.1  Milk  1.03 

Glass  2.4-4.5  Fresh  water  1.00 

Marble  2.5-2.8  Kerosene  0.8 

Granite  2.5-3.0  Gasolene  0.7 

Aluminum  2.65  Air  about  0.0012 


10  PRACTICAL  PHYSICS 

14.  Measurement  of  density.  The  simplest  way  to  deter- 
mine the  density  of  a  substance  is  to  weigh  the  substance 
and  measure  its  volume. 

Thus  a  piece  of  pine  6  feet  long,  1  foot  wide,  and  6  inches  thick  has  a 
volume  of  3  cubic  feet.  If  it  weighs  90  pounds,  its  density  is  30  pounds 
per  cubic  foot. 

An  empty  kerosene  can  weighs  1.25  pounds,  and  when  filled  with  kero- 
sene, it  weighs  36.25  pounds,  so  that  the  net  weight  of  the  kerosene  in  the 
can  is  35  pounds.  If  the  can  holds  5  gallons,  the  density  of  the  kero- 
sene is  7  pounds  per  gallon. 

A  block  of  steel  is  15  centimeters  long,  6  centimeters  wide,  and  1.5 
centimeters  thick  and  weighs  1050  grams  ;  then  the  density  is  *£$>-  or 
7.8  grams  per  cubic  centimeter. 

From  the  preceding  examples  it  will  be  seen  that  the 
density  of  a  body  is  found  by  dividing  its  weight  by  its 
volume.  In  other  words, 

weight 


It  is  also  evident  that  if  we  know  the  density  of  a  substance, 
we  can  compute  the  weight  of  any  volume  of  the  substance. 
It  is  by  this  method  that  engineers  calculate  the  weight  of 
buildings  and  bridges  which  it  would  be  impossible  to  weigh. 
For  example,  an  engineer  finds  that  a  reenforced  concrete 
pier  contains  2500  cubic  feet  of  material,  and  he  knows  that 
such  material  averages  150  pounds  per  cubic  foot.  Then 
the  weight  of  the  pier  is  equal  to  2500  times  150,  or  375,000 
pounds,  or  about  188  tons.  In  other  words, 

Weight  =  density  x  volume. 

If  it  is  the  volume  of  anything  that  we  want  to  know,  we 
have 


Volume  =5«. 
A  density 


INTRODUCTION:     WEIGHTS  AND  MEASURES 


11 


PROBLEMS 

(Use  data  given  in  table  on  page  9  when  necessary.) 

1.  A  block  of  iron  is  10  centimeters  by  8  centimeters  by  5  centime- 
ters, and  weighs  3  kilograms.     What  is  its  density  expressed  in  grams 
per  cubic  centimeter? 

2.  A  block  of  stone  measures  4  feet  by  2  feet  by  15  inches,  and 
weighs  1625  pounds.     Find  its  density  in  pounds  per  cubic  foot. 

3.  How  many  pounds  does  1  cubic  foot  of  aluminum  weigh  ? 

4.  The  cork  in  a  life  preserver  weighs  20  pounds.     What  is  its  vol- 
ume in  cubic  feet? 

5.  A  flask  with  a  capacity  of  120  cubic  centimeters  is  filled  with 
mercury.     How  many  kilograms  of  mercury  does  it  hold? 

6.  A  quart  bottle  is  weighed  empty  and  then  full  of   milk.     How 
many  pounds  should  it  gain  in  weight? 

7.  A  cylindrical  railway  water  tank  measures  on  the  inside  10  feet 
in  depth  and  6  feet  in  diameter.     How  many  tons  of  water  doos  it  hold? 

8.  A  piece  of  platinum  wire  is  12.5  centimeters  long  and  0.8  milli- 
meter in  diameter.     How  much  would  it  cost  if  the  price  of  platinum  is 
$1.00  per  gram? 

9.  If  a  certain  copper  telephone  wire  is  0.165  inch  in  diameter, 
what  does  a  mile  of  the  wire  weigh  ? 

10.    The  inside  diameter  of  a  lead  pipe  is  1  inch,  and  the  wall  is  0.25 
inch  thick.     How  many  pounds  does  it  weigh  per  foot? 

15.   The  three  fundamental  units. 

On  account  of  its  more  convenient 
size,  the  centimeter,  instead  of  the 
meter,  is  universally  used  in  scien- 
tific work  as  the  fundamental  unit 
of  length.  For  a  similar  reason,  the 
gram,  instead  of  the  kilogram,  is 
used  as  the  fundamental  unit  of 
weight.  The  second  is  taken  among 
all  civilized  nations  as  the  standard 
unit  of  time.  It  is  -^ToTr  °^  tne 
time  from  noon  to  noon. 

The  process  of   weighing   some- 
thing on   a   balance    is   quite   dis-  FIG.  7.  —  Stop  watch. 


12  PRACTICAL  PHYSICS 

tinct  from  the  measurement  of  a  length,  and  the  measure- 
ment of  time  is  wholly  different  from  the  measurement  either 
of  length  or  weight.  Moreover,  each  is  done  with  a  distinct 
sort  of  instrument.  In  a  time  measurement  the  instrument 
is  a  clock  or  watch.  For  short  intervals  of  time  a  special 
type  of  watch  is  used,  known  as  a  stop  watch  (Fig.  7). 

It  is  found  that  the  measurement  of  any  quantity,  such  as 
the  steam  pressure  in  a  boiler,  the  speed  of  an  express  train, 
or  the  loudness  of  a  foghorn,  can,  in  the  ultimate  analysis, 
be  reduced  to  measurements  of  length,  weight,  and  time. 
The  units  of  length,  weight,  and  time  are  therefore  the  three 
fundamental  units  of  physics. 

SUMMARY   OF  PRINCIPLES   IN   CHAPTER  I 
weight 


Density  = 

volume 

QUESTIONS  * 

1.  What  is  the  origin  of  the  prefixes  deci,  centi,  and  milli,  used  in  the 
metric  system? 

2.  How  could  you  determine  the  volume  of   an  irregular  piece  of 
rock  by  means  of  a  graduated  cylinder  partly  filled  with  water? 

3.  How  would  you  measure  the  diameter  of  a  steel  ball  ? 

4.  How  does  your  local  jeweler  get  "  standard  time  "  to  set  his  clocks 
and  watches  correctly? 

5.  How  can  the  thickness  of  this  sheet  of  paper  be  measured? 

6.  What  is  the  difference  between  a  ship's  chronometer  and  a  dollar 
alarm  clock  ? 

7.  Why  is  it  that  the  United  States  and  Great  Britain  are  the  only 
two  civilized  countries  that  do  not  use  the  metric  system  commercially  ? 

*  In  trying  to  find  the  answers  to  these  questions,  the  student  is  expected 
to  consult  various  reference  books,  such  as  dictionaries,  encyclopedias,  en- 
gineering handbooks,  and  popular  science  magazines..  He  is  also  expected 
to  keep  his  eyes  open  outside  of  the  classroom,  and  to  ask  questions  of  me- 
chanics and  tradespeople. 


CHAPTER  II 


SIMPLE  MACHINES 

Levers  of  various  kinds  —  principle  of  moments — force  at 
.  the  fulcrum  —  weight  of  a  lever  —  center  of  gravity  in  general 
—  wheel  and  axle  —  pulley  systems  —  parallel  forces. 

Work  —  principle  of  work  —  differential  pulley  —  inclined 
plane  —  wedge  —  screw  —  combinations  of  simple  machines  — 
power  —  transmission  of  power. 

Friction  —  so-called  "  laws  of  friction  "  —  coefficient  of  fric- 
tion—  advantages  of  friction  —  rolling  friction  —  efficiency  of 
machines. 

16.  Why  we  use  machines.     A  man  can  lift  a  piano  up 
to  a  window  on  the  second  floor  with  a  rope  and  tackle.     A 
boy  can  roll  a  barrel  of  flour  up  into  a  wagon  with  a  skid. 
A  girl  can  pull  a  nail  out  of  a  box  with  a  claw  hammer  al- 
though she  could  not  move  the  nail  at  all  with  her  fingers 
alone.     It  is  obvious  that  we  can  do  many  things  with  simple 
machines  that  it  would  be  quite  impossible  for  us   to  do 
without  them  because  we  are  A  T  B 

not  strong  enough.  Further- 
more, some  machines  enable  us 
to  do  things  more  quickly  or 
more  conveniently  than  we 
could  without  them.  Most 
important  of  all,  we  often  use 
machines  in  order  to  make  use 
of  forces  exerted  by  animals, 
wind,  water,  or  steam. 

17.  Equal-arm     lever.  — 
Doubtless    the   simplest   ma- 
chine is  the  lever  with  equal 

13 


FIG.  8.  —  Equal-arm  lever. 


14  PRACTICAL   PHYSICS 

arms,  such  as  a  seesaw,  or  the  walking  beam  on  a  steamboat, 
or  the  scale  beam  on  a  platform  balance.  In  this  case  we 
know  that  equal  weights  or  equal  forces  just  balance  when 
placed  at  equal  distances  from  the  point  of  support.  Thus 
in  figure  8,  when  Wl  equals  TF2,  the  distance  AF  must  equal 
the  distance  BF.  In  the  technical  language  of  physics  the 
point  of  support  (^)  of  a  lever  is  called  its  fulcrum. 

18.  Unequal-arm  lever.  Very  often  the  distances  of  the 
weights  from  the  fulcrum  are  not  equal.  For  example,  the 
distances  are  unequal  when  two  persons  of  unequal  weight 
are  seesawing,  or  in  the  case  of  an  ordinary  pump  handle. 
It  is  evident  that  at  equal  distances,  the  larger  weight  would 
have  the  greater  tendency  to  tip  the  lever,  and  also  that,  with 
equal  weights,  the  weight  at  the  greater  distance  from  the 
fulcrum  has  the  greater  tendency  to  tip  the  lever.  There- 
fore in  order  to  have  two  unequal  weights  balance,  they 
must  be  so  placed  that  the  smaller  weight  is  at  the  greater 
distance  from  the  fulcrum. 


40cm  F 


50  ^  100 g 


7 


FIG.  9.  —  Two  unequal  forces. 

If  we  balance  an  ordinary  meter  stick  in  the  middle  and  suspend  a 
50-gram  weight  (W^)  at  A,  which  is  40  centimeters  from  the  fulcrum 
(F),  and  then  hang  a  100-gram  weight  (W2)  on  the  other  side  at  such  a 
point  as  just  to  balance  the  first  weight,  we  shall  find  that  the  point  B 
where  the  100-gram  weight  is  hung  is  about  20  centimeters  from  F  or 
half  as  far  from  the  fulcrum  as  the  50-gram  weight. 

Careful  experiments  show  that  any  two  unequal  forces 
will  balance  only  if  the  force  on  one  side  multiplied  by  the  per- 
pendicular distance  of  its  line  of  action  from  the  fulcrum  equals 


SIMPLE  MACHINES 


15 


the  force  on  the  other  side  multiplied  by  the  distance  of  its  line 
of  action  from  the  fulcrum.  For  example,  in  figure  9, 

W1  x  AF=  Wt  x  BF. 

This  relation  of  the  forces  and  distances  may  also  be  ex- 
pressed by  a  proportion 

W1:   W2::  BF :  AF, 

which  may  be  stated  in  words  as  follows :  the  forces  are 
inversely  proportional  to  their  distances  from  the  fulcrum. 
This  means  that  if  one  force  is  three  times  as  great  as  another, 
then  its  line  of  action  must  be  one  third  as  far  away  from  the 
fulcrum  as  the  other  to  make  the  lever  balance. 

Crowbars,  shears,  glove  stretchers,  pliers,  etc.,  are  all  ex- 
amples of  this  sort  of  lever. 

19.  One-arm  lever.  When  the  fulcrum  is  located  at  one 
end  of  the  lever,  as  in  figure  10,  the  same  principle  is  in- 
volved. There  are  two  tendencies  which  must  balance,  the 
tendency  of  the  weight  to  tip  the  lever  down  and  the  tend- 
ency of  the  pull  applied  to  the  lever  to  lift  it  up.  The 
weight  multiplied  by  the  perpendicular  distance  from  the 
fulcrum  to  its  line  of  action  measures  its  turning  effect  about 
the  fulcrum;  that  is,  its  tendency  to  tip  the  lever  down. 
This  must  be  balanced  by  an  equal  turning  effect  in  the 
opposite  direction,  namely,  the  upward  pull  multiplied  by  its 

distance  from  the  fulcrum. 

p 


FIG.  10.  —  One-arm  levers. 


Suppose  we  fasten  a  stick  (Fig.  10)   by  a  screw  (F)  to  an  upright 
support,  so  that  the  stick  is  free  to  turn,  and  hang  a  weight  (W),  say  10 


16 


PRACTICAL  PHYSICS 


pounds,  at  a  distance  of  6  inches  from  the  fulcrum  (F)  Then  if  we 
pull  up  with  a  spring  balance  at  a  point  (B)  12  inches  from  the  ful- 
crum (F),  we  shall  find  that  the  pull  measured 

W  ^r^~-MB&  by  fche  sPring  balance  is  about  5  pounds.  (Of 
course  allowance  has  to  be  made  for  the  weight 
of  the  stick.) 

FIG.  11.  — Nutcracker.  m,  ,. 

1  he  equation  representing  these  tend- 
encies to  turn  the  stick  in  opposite  directions  would  be  as 
before 

=Px  BF. 


It  is  also  evident  that  if  the  10-pound  weight  ( W )  were 
hung  12  inches  from  the 
fulcrum 


FIG.  12.  —  Crowbar. 


>,  and  the  up- 
ward pull  applied  6  inches 
from  the  fulcrum,  the  pull 
needed  would  be  20  pounds. 
In  other  words,  the  same 
principle  applies  to  the  one- 
arm  lever  wherever  the 
weight  and  the  upward  pull  are  applied. 

A  nut  cracker  (Fig.  11),  a  crow  bar  when  used  with  one 

end  on  the  ground  (Fig.  12),  and 
the  forearm  (Fig.  13)  when  it  sup- 
ports a  weight  in  the  extended 
hand  are  examples  of  levers  with 
the  fulcrum  at  one  end,  or  one- 
arm  levers. 

20.  Lever  with  two  weights. 
The  ordinary  wheelbarrow  is  a 
good  example  of  a  one-arm  lever. 

.  The  fulcrum  is  located  at  the  axle 

of   the    wheel,  the   weight  is  the 

w  '•  load  carried,  and  the  upward  pull 

FIG.  13.— Forearm.  is  exerted  on  the  handles  by  the 


SIMPLE  MACHINES 


17 


man.  In  practice,  however,  it  often  happens  that  the  load 
consists  of  two  weights,  such  as  two  bags  of  cement  or  two 
boxes  or  kegs,  as 
shown  in  figure 
14.  To  get  the 
upward  pull  we 
have  merely  to 
compute  the  turn- 


FIG. 14.  —  Wheelbarrow  with  two  weights. 


ing  effect  of  each 

of   the   weights 

(TP^  and  W%)  about  the  fulcrum  (JF7)  and  make  the  sum  of 

these  effects  equal  to  the  turning  effect  of  the  upward  pull 

(P).     That,  is,. 

W1  x  BF+  W2  x  AF=  P  x  OF. 

In  general,  then,  we  see  that  we  can  balance  the  turning 
effect  of  two  or  more  weights  by  multiplying  each  weight  by 
the  perpendicular  distance  of  its  line  of  action  from  the 
fulcrum,  and  making  the  sum  of  these  products  equal  to  the 
product  of  the  pull  by  the  perpendicular  distance  of  its  line 
of  action  from  the  fulcrum. 

21.  Principle    of   moments.     It    has  been   seen   that   the 
turning  effect  of  a  force  depends  on  two  factors,  the  amount 
of  the  force  and  the  distance  of  its  line  of  action  from  the 
fulcrum.     This  product  —  force  times  perpendicular  distance  to 
fulcrum  —  is  called  the  moment  of  the  force.     For  a  lever  to  be 
in  equilibrium,  the  sum  of  the  moments  of  the  forces  tending 
to  turn  it  in  one  direction  must  equal  the  sum  of  the  moments 
of  the  forces  tending  to  turn  it  in  the  opposite  direction. 

22.  Force  at  the  fulcrum.      It  must  not  be  forgotten  that 
in  examples  of  the  lever,  the  fulcrum  itself  exerts  a  force, 
that  is,  a  push  or  a  pull.      When  the  fulcrum  is  between  the 

'two  weights,  it  evidently  has  to  push  up  an  amount  equal  to 
the  sum  of  the  weights  ;  that  is  (Fig.  15,  top),  F  —  W1  -f-  Wy 

\ 


18  PRACTICAL  PHYSICS 

When  the  fulcrum  is  at  one  end  of  the  lever,  and  the  pull  at 
the  other  end,  it  is  clear  that  the  fulcrum  must  exert  an  up- 
ward   push,    which   must 
ibe    such   that  it  and  the 
upward  pull  (P)  are  to- 
1       gether    equal     to    the 

weight.  That  is  (Fig. 
15,  middle),  W=F+P. 
When  the  fulcrum  is  at 
one  end  and  the  weight 
at  the  other  end,  it  will 
be  readily  seen  that  the 
fulcrum  has  to  push  down- 
ward and  that  the  upward 
pull  (P)  must  equal  the 
sum  of  this  downward 
push  at  F  and  the  weight 
W.  That  is  (Fig.  15, 
bottom),  P  =  W+  F.  In 
short,  it  will  be  seen  that 
in  all  these  cases  the  sum 
of  the  forces  pulling  up 


FIG.  15.— Force  exerted  by  fulcrum  of  lever,     must     equal     the     8Um     of 

the  forces  pulling  down. 
PROBLEMS 

1.  Identify  the  fulcrum,  and  the  direction  of  the  two  forces,  in  the 
case  of  a  pair  of  shears,  a  glove  stretcher,  a  pair  of  tongs,  and  a  nut 
cracker,  regarded  as  examples  of  the  lever,  and  think  of  other  examples. 

2.  What  weight  placed  20  inches  from  the  fulcrum  will  balance  100 
pounds  placed  8  inches  away  on  the  opposite  side?     What  is  the  pressure 
on  the  fulcrum  ? 

3.  In  figure  9  the    movable   weight   on    an   old-fashioned  steelyard 
weighs  3  pounds,  and  is  placed  at  such  a  distance  as  to  balance  a  50-pound 
sack  which  is  hung  from  a  point  1  inch  from  the  point  of  support.     How 
far  from  the  point  of  support  must  the  sliding  weight  be  placed  ? 


SIMPLE  MACHINES 


19 


4.  A  piece  of  wire,  which  is  to  be  cut  with  shears,  is  placed  0.5  inch 
from  the  rivet.     If  a  force  of  25  pounds  is  applied  on  the  handles  6  inches 
from  the  rivet,  how  much  force  is  exerted  on  the  wire  ? 

5.  A  plank  12  feet  long  is  to  be  used  as  a  seesaw  by  two  boys  who 
weigh  100  pounds  and  140  pounds.     How  far  from  the  lighter  boy  must 
the  prop  be  placed  ? 

(HINT.  —  Let  x  =  distance  from  small  boy  and  12  —  x  =  distance  from 
big  boy.) 

6.  The  handles  of  a  wheelbarrow  (Fig.  10)  are  4  feet  6  inches  from 
the  axle,  and  the  load  of  200  pounds  can  be  considered  as  18  inches  from 
the  axle.     How  much  effort  must  be  exerted  to  raise  the  handles? 

23.  Bent  lever.  Consider  next  a  claw  hammer  (Fig.  16) 
with  a  12-inch  handle.  If  a  60-pound  pull  (P)  at  B  is 
necessary  to  pull  the  nail  at  A,  which  is 
1.5  inches  from  F,  what  is  the  resistance 
(R)  which  the  nail  offers  ?  The  moment 
of  P  is  P  X  BF,  and  the  moment  of  R 
is  R  x  AF,  therefore  60  x  12  =  R  x  1.5, 
and  R  =  480  pounds.  In  this  case  it  will 
be  seen  that  the  two  arms  of  the  lever  are 

inclined  to  each  other, 

but    the  principle  of 

moments  applies  just 

as  if  it  were  a  straight 

lever.    The  bent  lever 

is  very  common  as  a 

part  of  a  machine. 

A  great  many  other  objects  can  be  regarded 
as  bent  levers.  For  example,  suppose  a  door 
(Fig.  17)  8  feet  high  and  4  feet  wide,  weighing 
60  pounds,  swings  on  hinges  placed  1  foot  from 
the  top  and  1  foot  from  the  bottom,  (a)  What 
is  the  vertical  pressure  on  each  hinge?  If  the 
door  is  properly  hung,  the  weight  will  be  equally 
divided  between  the  two  hinges,  and  each  hinge 
will  support  30  pounds.  (6)  How  great  is 


-Pi 

^t 

J 

G.  1 

L" 
xz 

7 

7.—  Doorasabeut 
lever. 

FIG.   16.  — Hammer  as 
a  bent  lever. 


20  PRACTICAL  PHYSICS 

the  horizontal  pull  on  the  upper  hinge?  If  we  consider  the  entire 
weight  of  the  door  as  acting  at  its  center,  then  the  moment  of  this 
weight  about  the  lower  hinge  will  be  2  times  60,  or  120.  The  moment 
of  the  pull  exerted  by  the  upper  hinge,  reckoned  about  the  lower  hinge, 
will  be  6  times  the  pull.  Making  these  two  moments  equal,  we  find  that 
the  pull  is  20  pounds,  (c)  In  a  similar  way,  by  considering  the  upper 
hinge  as  a  fulcrum,  we  may  compute  the  push  exerted  by  the  lower 
hinge,  which  also  equals  20  pounds. 

24.  Center  of  gravity.     So  far  in  our  study  of  levers  we 
have  assumed  that  the  weight  of  the  lever  itself  could  be 
neglected,  but  in  practice  this  is  not  always  the  case.     It  is 
our  problem  now  to  find  how  to  make   allowance  for  the 
weight  of  the  lever. 

We  have  already  seen  that  a  lever  carrying  two  weights 

(Fi£*  18)  can  be 
supported  at  a 

point  in  between, 
which  we  have 
called  the  fulcrum, 
but  which  we  may 

FIG.  18.  -  Center  of  gravity  of  two  ^ightl  now  cal1  the  "  cen~ 

ter  of  gravity" 
or  "center  of  weight."  The  force  necessary  to  support  this 
point  is  the  same  as  if  the  whole  weight  were  concentrated 
there.  In  the  same  way  we  could  support  a  bar  carrying 
three  or  more  weights  on  a  single  fulcrum,  if  it  is  placed  at 
the  right  point.  That  point  would  be  the  center  of  gravity 
of  the  weights.  In  general,  everything  has  a  center  of  grav- 
ity at  which  we  can  consider  its  whole  weight  concentrated. 
To  find  the  position  of  the  center  of  gravity,  we  have  simply 
to  find  the  point  at  which  the  object  would  balance  on  a 
knife  edge.  This  may  be  computed,  but  it  is  usually  easier 
to  locate  it  experimentally. 

25.  How  to  find  a  center  of  gravity  by  experiment.     If  the 
shape  of  the  object  is  simple  and  its  density  is  everywhere 
the  same,  as  in  the  case  of  a  shaft  or  a  board,  we  should  ex- 


SIMPLE  MACHINES 


21 


pect  the  center  of  gravity  to  be  in  the  middle,  and  if  we  try 
to  balance  the  object  on  some  sharp  edge,  we  find  that  the 
center  of  gravity  is  indeed  located  at  the  geometrical  center. 
In  the  case  of  an  irregularly  shaped  object  like  a  baseball 
bat,  the  simplest  way  is  to  balance  the  bat  on  a  knife  edge. 
In  the  case  of  a  chair,  the  center  of  gravity  may  be  found  by 
considering  that,  if  the  chair  is  hung  so  as  to  swing  freely, 
the  center  of  gravity  will  lie  directly  under  the  point  of 
suspension.  Therefore,  if  a  chair,  or  any  irregular  object, 
is  hung  from  two  points  successively,  the  point  of  intersec- 
tion of  the  plumb  lines  from  these  points  will  locate  the 
center  of  gravity. 

To  make  this  clear,  let  us  take  an  irregular  sheet  of  zinc  and  drill 
three  holes  near  the  edge,  A,  B,  and  C,  in  figure  19.  Let  the  zinc  be 
hung  from  a  pin  put  through  the,  hole 
A  and  let  a  plumb  line  be  also  hung  from 
the  pin.  Draw  a  line  on  the  zinc  to 
show  where  the  plumb  line  crosses  it. 
Then  let  the  zinc  be  hung  from  another 
hole  and  draw  another  line  in  a  similar 
way.  The  point  of  intersection  is  the 
center  of  gravity.  When  the  zinc  is 
hung  from  the  third  hole,  the  plumb 
line  will  pass  through  the  center  of  grav- 
ity already  found. 


FIG.  19. —Finding  center  of 
gravity. 


In  the  case  of  a  ring,  or  a  cup, 
or  a  boat,  the  center  of  gravity 
will  not  lie  in  the  substance  itself,  but  in  the  empty  space 
inside ;  but  this  will  not  bother  [us  in  answering  questions 
about  how  such  objects  act.  We  -may,  if  we  like,  think 
of  such  a  center  of  gravity  as  rigidly  attached  to  the  object 
by  a  very  light,  stiff  framework. 

We  shall  find  this  idea  of  the  center  of  gravity  especially 
convenient  in  problems  where  the  weight  of  a  lever  has  to 
be  considered,  for  we  can  now  assume  that  the  whole  weight 
of  the  lever  is  concentrated  and  acting  at  its  center  of  gravity. 


22  PEACTICAL  PHYSICS 

Suppose  that  an  18-ounce  hammer  balances  10  inches  from  the  handle 
end.  When  a  fish  is,  tied  to  the  end  of  the  handle,  the  whole  balances 
.6  inches  from  the  end.  How  much  does  the  fish  weigh?  We  may  con- 
sider the  weight  of  the  hammer,  18  ounces,  as  concentrated  at  a  point 
10  inches  from  the  end  of  the  handle  or  4  inches  from  the  fulcrum.  Let  x 
be  the  weight  of  the  fish,  which  is  applied  6  inches  from  the  fulcrum. 
Then  we  have  'V 

6z  =  4x  18, 
x  =  12  ounces,  the  weight  of  the  fish. 

PROBLEMS 

* 

1.  A  boy  has  a  2-pound  fish  pole  10  feet  long,  the  center  of  gravity 
of  which  is  3.5  feet  from*  the  thick  end.     He  finds  the  weight  of  his 
string  of  fish  by  hanging  them  from  the  thick  end  of  the  pole  and  then 
balancing  .the  pole  J>n  a^ence  rail,  t  He  finds«that  it  balances  at  a  point 
15  niches  from  th»  end.     feow  many  pounds  of  fish  has  he? 

2.  A  pole  20  feet  long* weighs  120  fjoundft^.     When  a  30-pound  bag  of 
meal  is  hung  q£  one  en,d, ^hfe  balancing  point  is  3  feet  from  the  same 
end.     Where  is  the  center  of  gravity  of  the  pole? 

3.  A  6-foot  crowbar  balances  at  a  point  2.5  feet  from  its  sharp  end. 
If  a  weight  of  30  pounds  is  hung  0.5  feet  from  this  end,  and  50  pounds 
is  hung  1  foot  from  the  other  end,  it  balances  at  its  mid-point.     How 
heavy  is  the  bar  ? 

4.  A  uniform  beam  AB,  20  feet  long,  weighing  600  pounds,  is  sup- 
ported by  props  placed  under  its  ends.     Four  feet  from  prop  A,  a  weight 
of  200  pounds  is  suspended.     Find  the  pressure  on  each  prop. 

(HINT.  —  Regard  as  a  lever,  with  its  fulcrum  at  one  end.) 

5.  A  rectangular  gate  3.5  feet  high  and  5  feet  wide  has  its  center  of 
gravity  at  its  geometrical  center.     It  is  hung  on  hinges  placed  3  inches 
from  the  top  and  bottom.     The  gate  weighs  100  pounds,     (a)  What 
vertical  pressure  should  each  hinge  sustain  ?     (b)  What  is  the  horizontal 
pull  on  the  upper  hinge  ?     (c)  What  is  the  horizontal  push  against  the 
lower  hinge? 

26.  Wheel  and  axle.  A  special  form  of  lever  consists  of  a 
wheel  or  crank  which  is  fastened  rigidly  to  an  axle  or  drum. 
The  weight  to  be  lifted,  or  the  resisting  force  of  whatever 
kind,  is  generally  applied  to  the  axle  by  means  of  a  rope  or 
chain,  and  the  "  effort,"  or  pull,  is  exerted  on  the  rim  of  the 


SIMPLE  MACHINES 


23 


wheel,  as  shown  in  figure  20.  In  calculating  the  effort  (P) 
needed  to  balance  a  given  resistance  (  TF)  we  have  merely  to 
take  moments  about  the  center  (.F)  of  the 
wheel  and  axle.  If  we  call  the  radius  of  the 
wheel  R  and  that  of  the  axle  r,  then, 


Weight  x  axle^ 
or 


or 


r-r<^^^= 


=  effort  x  wheel-radius 
PxK, 


PaV, 


FIG.  20.— Wheel 
and  axle. 


27.  Uses  of  the  wheel 
and  axle.  A  windlass 
used  in  drawing  water 
from  a  well  (Fig.  21)  by  means  of  a 
rope  and  bucket  is  an  application  of 
the  principle  of  the  wheel  and  axle. 
In  the  windlass,  a  crank  takes  the  place 
of  a  wheel,  and  the  length  of  the  crank 
is  the  radius  of  the  wheel. 

If  a  wheel  is  used  in  turning  the  rudder 
of  a  boat,  the  rope  attacned  to  the  rudder 
is  wound  round  the  axle,  and  the  steersman  applies  his  effort 
to  the  handles  which  project  from  the  rim  of  the  wheel  (  Fig.  22). 

In    the     derrick      (Fig.      23), 
which  is  used  in    lifting   heavy 


FIG.  21.  — Windlass  for  a 
well. 


FIG.  22.  —  Steering  wheel  in  a  boat. 


FIG.  23.  —  Hoisting  derrick. 


24 


PRACTICAL  PHYSICS 


weights,  we  usually  have  a  double  wheel  and  axle.  The 
effort  of  the  workmen  is  applied  at  the  cranks,  which  are  at- 
tached to  one  axle.  This  then  drives,  through  a  spur  gear, 
a  wheel  on  a  second  axle. 

28.  The  pulley.  The  fixed  pulley,  shown  in  figure  24,  con- 
sists of  a  wheel  with  a  grooved  rim,  called  a  sheave,  free  to 
rotate  on  an  axle  which  is  suppor^M^a  fixed  block.  A 
flexible  rope  or  cable  passes  over  ll  Bel.  Tt  is  evident 

.  ////////////////////////////////////////// 


FIG.  24.  —Fixed  pulley. 


FIG.  25.  —  Movable  pulley. 


that  if  equal  weights  or  equal  forces  are  applied  to  the  ends 
of  the  rope,  they  just  balance  each  other.  That  is,  the  effort 
P  is  equal  to  the  resistance  W.  So  there  is  no  advantage  in 
the  fixed  pulley,  except  that  it  is  sometimes  more  convenient 
to  exert  a  certain  pull  downwards  rather  than  upwards. 

Oftentimes  the  block  is  attached  to  the  weight  to  be  lifted, 
as  shown  in  figure  25,  and  then  it  is  called  a  movable  pulley. 
Here  the  effort  P  is  not  equal  to  the  weight  W,  for  it  will 
be  seen  that  the  load  IF"  is  supported  by  two  ropes,  and  there- 
fore each  exerts  a  pull  equal  to  one  half  the  weight.  That 


=          or 


SIMPLE  MACHINES 


25 


The  ratio  of  the  weight  or  resistance  to  be  overcome  to  the 
effort  put  forth  is' called  tJu-  mechanical  advantage  of  a  machine. 
Fof^ekample,  the  mechanical  advantage  of  a  single  fixed 
pulley  is  1  and  of  a  single  movable  pulley  is  2. 

29.  Combinations  of  pulleys.     In  practical  work  it  is  quite 
common  to  use  a  fixed  block  witji  two  sheaves  and  a  movable 
block  with  two  sheaves,  as  shown  in  figure 

26.  One  end  of  the  rope  is  attached  to  the 
fixed  block,  and  the  effort  is  applied  to  the 
other  end  of  the  rope.  Let  us  compute  the 
relation  between  the  weight  to  be  lifted  and 
the  effort  applied.  From  figure  26  it  will 
be  seen  that  the  weight  and  the  movable 
block  are  supported  by  four  ropes,  and  so 
the  pull  on  each  rope,  neglecting  the  weight 
of  the  block,  is  one  fourth  the  weight  W. 
It  will  also  be  seen  that  the  pull  P  is  equal 
to  that  in  each  of  the  ropes,  since  a  pulley 
only  changes  the  direction  of  the  pull.  There- 
fore p  _  i  jjr  FIG.  26.  —  Double 

blocks. 

and  the  mechanical  advantage,  JF/P,  is  4. 

This  means  that,  neglecting  friction  and  the  weight  of  the 
movable  block,  a  pull  of  100  pounds  applied  at  P  would  just 
balance  a  weight  of  400  pounds  at  W. 

In  general,  we  can  find  the  mechanical  advantage  of  any 
combination  of  pulleys  by  counting  the  number  of  ropes  which 
support  the  weight. 

30.  Parallel  forces.     Suppose  we  have  a  3000-pound  auto- 
mobile standing  on  a  bridge  in  a  position  one  fourth  of  the 
length  of  the  bridge  from  one  end  (Fig.  28),  and  we  wish  to 
know  how  much  of  the  weight  is  borne  by  the  supports  at 
each  end  of  the  bridge. 

First  let  us  try  a  very  simple  experiment  which  will  make 
clear  the  principles  involved  in  this  problem. 


26 


PRACTICAL   PHYSICS 


I 


Nail 


FIG.  27. —  Parallel  forces, 
move  now.     But  we  can  now  think  of  the  stick  as 


Hang  a  light  stick  (Fig.  27)  by  two  or  more  stirrups  attached  to 
spring  balances  (A,  B,  C),  and  let  several  weights  (Z>,  E}  be  hung  from 

it  at  various  points.  If  the  sup- 
ports do  not  break,  the  stick 
will  remain  suspended  mo- 
tionless indefinitely.  The 
sum  of  the  forces  pulling  up 
is  equal  to  the  sum  of  the 
forces  pulling  down.  Now 
suppose  that  there  happen  to 
be  several  holes  through  the 
stick  and  that  a  nail  is  care- 
fully driven  through  one  of 
them  into  the  wall  behind. 
If  the  stick  did  not  move 
before,  it  certainly  will  not 
lever  with  the  nail 
as  a  fulcrum,  and  it  is  in  equilibrium  about  that  nail.  This  means  that 
the  sum  of  the  moments  of  the  forces  tending  to  turn  it  in  one  direction 
equals  the  sum  of  the  moments  of  the  forces  tending  to  turn  it  in  the  op- 
posite direction. 

Evidently  this  nail  could  have  been  put  through  a  hole  at  any  point 
along  the  stick,  and  the  moments  calculated  around  that  point  would 
balance. 

This  example  and  section  22  show  that  when  several  paral- 
lel forces  are  in  equilibrium  two  conditions  must  be  fulfilled. 

(1)  The  sum  of  the  forces  pulling  in  one  direction  must  equal 
the  sum  of  those  pulling  in  the  opposite  direction. 

(2)  The  sum  of  the  moments  tending  to  rotate  the  whole  in 
one  direction  around  any  point  whatever  must  equal  the  sum  of 
the  moments  tending  to  rotate  the  whole  in  the  opposite  direction 
around  that  same  point. 

Let  us  apply  these 
principles  of  parallel 
forces  to  the  problem 
of  the  automobile 
standing  on  the  bridge. 
This  can  be  represented 
by  figure  28,  where  A 
is  the  weight  of  the 


. 
\ 


A  3000  Ibs. 


3x 


FIG.  28.  —  Bridge  with  automobile  on  it. 


SIMPLE  MACHINES 


27 


automobile,  and  B  and  C  are  the  upward  forces  exerted  by  the  end  sup- 
ports. We  know  one  force  (A  =  3000  pounds),  and  the  relative  dis- 
tances between  these  forces.  We  are  to  find  the  magnitudes  of  B  and  C. 
Since  B  +  C  =  3000,  C  -  3000  -  B.  Suppose  we  take  the  position  of  the 
automobile  as  the  point  about  which  to  compute  moments ;  then  we  have 

B  x3x  =  (3000  -  B)  x  x, 

B  =  750  pounds,  J5's  load, 
3000  -  B  =  2250  pounds,  C's  load. 

We  can  also  solve  this  problem  by  taking  moments  first  around  one 
end,  and  then  around  the  other.  Working  in  this  way,  we  do  not  need 
the  first  principle  at  all.  Do  this  and  see  if  you  get  the  same  answers. 

It  should  be  noticed  that  all  the  machines  so  far  considered, 
namely,  the  lever  (except  the  bent  lever),  the  wheel  and  axle, 
and  the  pulley,  are  simply  special  cases  of  parallel  forces,  and 
that  we  can  discover  anything  we  want  to  know  about  any 
of  them,  by  means  of  one  or  both  of  the  general  principles 
mentioned  just  above.  For  the  lever  and  the  wheel  and  axle, 
the  principle  of  moments  is  enough,  unless  we  want  to  know 
the  force  at  the  fulcrum.  For  that  we  need  the  first  principle. 
For  the  pulley  we  need  only  the  first  principle. 

PROBLEMS 

1.  The  diameter  of  an  axle  is  1  foot,  and  the  diameter 
of  the  circle  in  which  a  crank  on  the  axle  moves,  is  3  feet. 
If  150  pounds  is  the  weight  to  be  raised,  how  much  force 
must  be  applied  to  the  crank  ? 

2.  The  crank  on  a  grindstone  is  9  inches  long,  and  the 
diameter  of  the  stone  is  30  inches.     If  50  pounds  is  the 
force  applied  on  the  crank,  what  force  can  be  exerted  on 
the  rim  of  the  stone  ? 

3.  What  must  be  the  ratio  of  the  diameters  of  a  wheel 
and  axle,  in  order  that  150  pounds 

may  support  1  ton  ?     What  is  the 
mechanical  advantage? 

4.  Two  single  fixed  pulleys  are 
used  to  raise  a  barrel  of  flour,  as 

shown  in  figure  29.     If  a  barrel  of  FlG-  29-  —  Simple  pulley  system, 

flour  weighs  200  pounds,  how  much  does  the  horse  have  to  pull? 


28  PRACTICAL  PHYSICS 

5.  The  gaff  of  a  boat  is  to  be  raised  by  means  of  a  movable  single 
block  attached  to  it,  and  a  fixed  double  block  attached  to  the  top  of  the 
inast,   one   end  of   the   rope   being   tied  to  the  movable  block.      How 
much    resistance    can    be   overcome    by    100    pounds    exerted    on    the 
rope? 

6.  A  pair  of  triple  blocks  contain  three  sheaves  each.     The  rope  is 
attached  to  the  upper  fixed  block.     What  force  is  just  sufficient  to  bal- 
ance a  weight  of  1  ton,  neglecting  friction  ? 

7.  An   automobile   gets  stuck   in  the  sand.      In   order  to  pull   it 
out,  a   horse,  a  rope,  and  a  couple  of  triple  blocks  are  used.     If   the 
horse  exerts  a  steady  pull  of   500  pounds  on  the  rope,  and  one  block 
is    fastened    to    a    tree    and    the    other    to    the    machine,   how   much 
resistance  can  be  overcome?     Find  two  solutions  for  this  problem,  the 
rope  being  fastened  in  one  case  to  the  fixed  block,  and  in  the  other  to 
the  movable  block. 

8.  Two  boys,  A  and  B,  are  carrying  a  100-pound  load  slung  on  a 
pole  between  them.    Their  hands  are  10  feet  apart,  and  the  load  is  3  feet 
from  A.      How  much  does  each  carry?      Neglect  the  weight  of  the 
pole. 

9.  A  man  holds  a  shovelful  of  coal,  weighing  50  pounds,  with  his 
left  hand  at  the  end  of  the  shovel,  and  his  right  hand  22  inches  away. 
Supposing  the  center  of  gravity  of  the  shovel  and  coal  to  be  40  inches 
from  his  left  hand,  how  much  does  he  push  down  with  his  left  hand,  and 
how  much  does  he  pull  up  with  his  right  hand  ? 

10.  A  man  and  a  boy  carry  a  load  of  200  pounds  on  a  pole  8  feet  long. 
Where  must  the  load  be  placed  if  the  boy  is  to  bear  only  45  pounds 
of  it? 

31.  Work.  The  function  of  every  machine  is  to  do  a  certain 
amount  of  work.  Now  in  the  technical  language  of  science, 
work  means  the  overcoming  of  resistance.  For  example,  we  do 
work  when  we  lift  a  box  from  the  floor  to  the  table,  or  when 
we  push  the  box  along  the  floor  against  friction.  But  we 
are  not  doing  work  in  the  scientific  sense  of  the  word,  no 
matter  how  hard  we  push  or  pull,  if  we  do  not  lift  or  move 
the  box.  In  other  words,  work  is  measured  by  accomplish- 
ment, not  by  effort  or  by  fatigue. 

If  we  lift  one  pound  one  foot,  we  are  said  to  do  one  foot 
pound  of  work;  if  we  lift  5  pounds  3  feet,  we  do  15  foot 
pounds  of  work  ;  or  if  we  pull  hard  enough  on  a  box  to  lift 


SIMPLE  MACHINES  29 

5  pounds  and  thus  drag  it  3  feet,  we  still  do  15  foot  pounds 
of  work.     In  other  words, 

Work  (foot  pounds)  =  force  (pounds)  x  distance  (feet). 

It  should  be  remembered  that  the  distance  must  be  meas- 
ured in  the  same  direction  as  that  in  which  the  force  is  ex- 
erted. Thus,  if  a  machinist  exerts  upon  a  file  a  force  of  10 
pounds  downward  and  15  pounds  forward,  how  much  work 
will  he  do  in  40  horizontal  strokes,  each  6  inches  long? 
Evidently  the  total  distance  is  20  feet  and  the  horizontal 
force  is  15  pounds ;  therefore  the  work  done  is  300  foot 
pounds.  The  vertical  pressure  does  not  enter  into  the  cal- 
culation of  work  because  the  motion  is  horizontal. 

32.  Principle  of  work.  In  every  machine  a  certain  resist- 
ance is  overcome  by  a  certain  effort  exerted  on  another  part 
of  the  machine.  The  principle  of  work  which  applies  to  all 
machines  where  the  losses  due  to  friction  may  be  neglected, 
may  be  stated  as  follows:  The  work  put  into  a  machine  is 
equal  to  the  work  got  out.  In  short, 

Input  =  output. 

For  example,  in  the  wheel  and  axle  (see  Fig.  20,  section  26)  the 
output  is  equal  to  the  weight  times  the  distance  it  is  lifted,  and  the  input 
is  equal  to  the  effort  times  the  distance  through  which  it  is  exerted. 
For  convenience,  suppose  the  wheel  makes  just  one  turn.  Then  the  dis- 
tance the  weight  is  lifted  is  equal  to  the  circumference  of  the  axle,  2?rr, 
and  the  distance  through  which  the  effort  is  exerted,  is  the  circumference 
of  the  wheel.  2-jrR.  The  input  is  'P  x  2TrR,  and  the  output  is  W  x  2irr. 
Therefore,  by  the  principle  of  work, 

P  x  2irR  =  Wx2irr, 
or  P  x  R  =  W  x  r, 

which  is  exactly  the  equation  got  by  considering  the  wheel  and  axle  as  a 
modified  lever. 

Another  example  is  the  system  of  pulleys  shown  in  figure  26  in  sec- 
tion 29.  The  output  is  equal  to  the  weight  W  times  the  distance  it  is 
lifted,  and  the  input  is  equal  to  the  effort  P  times  the  distance  through 
which  it  is  exerted.  Suppose  the  distance  the  weight  W  is  lifted  is  D, 


30 


PRACTICAL  PHYSICS 


and  the  distance  through  which  the  effort  P  is  exerted  is  d.     The  outpui 
is  W  x  D  and  the  input  is  P  x  d.     Then,  by  the  principle  of  work, 


W  x  D  = 


or 


D 


But  when  the  weight  is  lifted  1  foot,  it  is  evident  that  each  of  the  sup- 
porting ropes  must  be  shortened  by  1  foot,  and  therefore  P  must  move  4 
feet  ;  in  other  words, 


Substituting  this  value  of  d  in  the  preceding  equation,  we  have 


which  is  the  same  as  the  result  which  we  got  by  considering  the  pulley 
as  a  case  of  parallel  forces. 

33.  The  differential  pulley.  In  shops  where  heavy  machin- 
ery is  to  be  lifted,  constant  use  is  made  of  the  differential  pulley, 

shown  in  figure  30.  This  con- 
sists of  two  sheaves  of  different 
diameters  in  the  upper  block 
rigidly  fastened  together,  and 
one  sheave  in  the  lower  block. 
An  endless  chain  runs  over 
these  blocks.  The  rims  of  the 
sheaves  have  projections  which 
fit  between  the  links  and  so 
keep  the  chain  from  slipping. 
Such  a  differential  pulley 
has  a  very  large  mechanical 

FIG.  30.  —  Differential  pulley.  advantage. 

To  see  just  now  it  comes  to  have  a  large  mechanical  advantage,  let  us 
set  up  such  a  pulley  and  study  it  carefully.  'When  the  chain  is  pulled 
down  as  shown  in  the  diagram,  it  is  wound  up  faster  on  the  large  fixed 
pulley  than  it  is  unwound  on  the  smaller  pulley.  In  order  to  compute 
the  mechanical  advantage  of  the  contrivance,  let  us  suppose  that  P  moves 


SIMPLE  MACHINES  31 

down  far  enough  to  turn  the  fixed  pulley  around  once.  If  R  is  the  radius 
of  the  large  fixed  pulley,  then  the  work  done  by  P  will  be  P  x  2  TrR.  If  r 
is  the  radius  of  the  small  fixed  pulley,  then  the  length  of  chain  unwound 
in  one  revolution  will  be  2  TIT.  The  weight  W  will  therefore  be  raised 
^(2-n-R  -  2  ?rr)  or  ir(R  -  r)  and  the  work  done  will  be  Wx-rr(R  -  r). 
Therefore,  if  we  neglect  losses  due  to  friction,  we  have 

W  x  7r(R  -  r)  =  P  x  2  7T/2, 

W       2R 
whence,  ^R^r' 

Since  the  difference  between  the  radii  of  the  two  fixed 
pulleys  (R  —  r)  is  small,  it  is  evident  that  the  mechanical 
advantage  is  large. 

The  differential  pulley  has  a  second  practical  advantage 
in  that  there  is  always  enough  friction  to  keep  the  weight 
from  dropping  when  the  force  P  is  released. 

PROBLEMS 

1.  A  man  carries  in  baskets  a  ton  of  coal  up  20  steps,  each  7  inches 
high.     How  much  work  does  he  do  on  the  coal  ? 

2.  In  the  metric  system,  work  is  measured  in  kilogram  meters.      How 
much  work  is  done  in  pumping  50  liters  of  water  40  meters  high  ? 

3.  A  man  weighing  150  pounds  raises  himself  up  a  mast  in  a  sling 
by  means  of  a  rope  passing  over  a  fixed  pulley  attached  to  the  top  of  the 
mast.     If  the  mast  is  100  feet  high,  how  much  work  does  he  do  ?     How 
hard  must  he  pull  ? 

4.  If  in  problem  1  on  page  27   the  weight   is  raised  10  feet,  how 
many  foot  pounds  of  work  are  done  by  the  machine  ? 

5.  If  in    problem  2  on  page  27   the  stone  is  turned   30  revolutions 
per  minute,  how  many  foot  pounds  of  work  are  put  into  the  grindstone 
per  minute  ? 

6.  In  a  certain  differential  pulley  the  large  wheel  is  6  inches  and  the 
small  wheel  5  inches  in  diameter.     What  is  the  mechanical  advantage? 

34.  Inclined  plane.  Barrels  and  casks  which  are  too  heavy 
to  lift  from  the  ground  into  a  wagon  are  often  rolled  up  a 
plank  or  skid.  This  is  an  example  of  what  is  called  an 
inclined  plane.  Every  street  or  road  which  is  not  level  is  an 
example  of  an  inclined  plane.  Experience  teaches  us  that 


32 


PEACTICAL  PHYSICS 


FIG.  31.— Inclined  plane. 


the  steeper  the  incline,  the  greater  the  pull  required  to  haul 
the  load  up  the  grade.     In  order  to  find  out  just  how  the 

effort  and  the  weight 
or  load  are  related  to 
the  grade,  let  us  try  a 
simple  experiment, 
where  friction  can  be 
neglected. 

Suppose  we  arrange  a 
very  smooth  plane,  such  as 
a  piece  of  plate  glass,  at  an 
angle,  as  shown  in  figure  31. 
Let  the  weight  or  load  (  W) 
be  a  heavy  metal  cylinder  which  turns  with  very  little  friction.  Attach 
to  the  cylinder  a  cord  and  pass  it  over  a  good  pulley  fastened  to  the  top  of 
the  plane,  and  then  hang  from  the  other  end  enough  weights  to  pull  the 
load  slowly  up  the  inclined  plane.  You  will  find  that  the  ratio  P/Wis 
approximately  the  same  as  the  ratio  H/L,  where  H  is  the  height  of  the 
incline  and  L  is  its  length. 

From  the  general  principle  of  work  we  can  also  arrive  at 
this  relation  of  effort  and  resistance  to  the  grade.  Suppose 
the  weight  W  is  rolled  from  the  bottom  to  the  top  of  the 
incline.  Then  it  has  been  lifted  .ZTfeet,  and  the  work  done 
is  W  (pounds)  times  H  (feet),  or  WJT  foot  pounds.  But 
while  the  weight  W  has  been  traveling  up  the  incline  whose 
length  is  L,  the  force  or  pull  P  has  moved  down  L  feet,  and 
the  work  put  in  is  equal  to  P  (pounds)  times  L  (feet),  or 
PL  foot  pounds.  Therefore,  if  we  neglect  friction,  we  have 


or 


W     L 


35.  The  grade  of  an  incline.  This  ratio  of  the  height  to 
the  length  of  an  incline  is  expressed  by  engineers  as  so  many 
feet  rise  per  hundred  feet  along  the  incline,  and  is  called 
the  grade  of  the  incline.  For  example,  suppose  a  road  rises 


SIMPLE  MACHINES  33 

5  feet  for  every  100  feet  along  the  incline,  then  this  road  is 
said  to  have  a  5  %  grade.  Since  a  3  %  grade  is  the  steepest 
allowable  on  a  really  good  road,  it  is  readily  seen  that  a 
small  force,  such  as  can  be  exerted  by  a  horse,  can  move  a 
much  heavier  load  up  a  gradual  incline  than  could  be  lifted 
directly.  For  this  reason  the  highways  in  mountain  regions 
are  laid  out  as  zigzags  and  switchbacks.  If  we  want  a 
flight  of  steps  easy  to  climb,  we  make  the  slope  gentle. 

Nevertheless  it  should  be  remembered  that  while  the  pull 
is  less  than  the  weight  of  the  load,  yet  the  distance  the  load 
travels  is  greater  than  when  it  is  lifted  straight  up.  In 
other  words,  what  we  gain  in  the  amount  of  effort  required 
we  lose  in  the  distance  over  which  it  must  be  exerted.  The 
total  work  to  be  done  is  independent  of  the  grade,  except  for 
the  indirect  effect  of  friction. 

36.  Wedge.     If  instead  of  pulling  the  load  up  the  incline, 
we  push  the  incline  under  the  load,  the  inclined  plane  is 
called  a  wedge.     Of  course  the  smaller  the  angle  of  the  wedge, 
the  easier  it  is  to  drive  it  against  the  resistance.     The  fact 
that  friction  plays  a  very  important  part  in  its  action  makes 
it  impossible  to  make  a  simple  statement  of  the  relation  of 
the  effort  required  to  force  in  a  wedge  to  the  resistance  to 
be  overcome. 

All  cutting  and  piercing  instruments,  such  as  the  ax,  the 
chisel,  and  the  carpenter's  plane,  as  well  as  nails,  pins,  and 
needles,  act  like  wedges.  The  carpenter  uses  wedges  to 
fasten  the  heads  of  hammers  and  axes  on  their  handles. 
The  woodsman  uses  wedges  to  split  logs  of  wood. 

37.  Screw.      When  an  enormous  force  must  be  exerted, 
as  in  lifting  a  building,  such  machines  as  the  lever,  pulley, 
and   inclined    plane   will    not   do,  because    we    cannot   get 
enough  mechanical  advantage.     A  screw,  such  as  the  jack- 
screw  (Fig.  32),  is  sometimes  used  for  this  purpose.     In  one 
complete  turn  of  the  screw,  the  weight  is  lifted  the  distance 
between  two  successive  threads,  which  is  called  the  pitch  of 


34 


PRACTICAL   PHYSICS 


the  screw,  while  the  effort  is  exerted  through  a  distance 
equal  to  the  circumference  of  the  circle  traced  by  the  end  of 
the  bar  or  handle.  In  each  complete  turn 
the  output  is  equal  to  the  weight  times  the 
distance  between  two  successive  threads, 
and  the  input  is  equal  to  the  effort  times 
the  distance  through  which  it  acts  ;  namely, 
the  circumference  of  a  circle. 

If  W  equals  the  weight  to  be  lifted  and 
p  (pitch)  equals  the  distance  between 
threads,  the  output  for  one  turn  is  TFtimes  p. 
FIG.  32.—  Jackscrew.  Let  P  equal  the  effort  or  force  applied  on 
the  handle,  and  2  irr  equal  the  circumfer- 
ence of  the  circle  in  which  it  acts.  Then  P  times  2  irr  is 
the  input.  Therefore  applying  the  principle  of  work  to  the 
machine,  we  would  have,  if  friction  could  be  neglected, 


W  X 


P   X    2  77T, 


p 


In  other  words,  the  mechanical  advantage  of  the  screw  is  equal 
to  the  ratio  of  the  circumference  of  the  circle  moved  over  by  the 
end  of  the  lever,  to  the  distance  between  the  threads  of  the 
screw. 

As  a  matter  of   fact,  friction  consumes  a  large   part  of 
the  work  put  in,  and  therefore  the  input  is 
greater  than  the  output.     But  this  loss  is  not 

wholly    a    disadvantage, 

for   it    keeps   the    screw 

from   turning   backward 

of  itself. 

38.    Applications  of  the 

screw.       We  are   all    fa- 
miliar with  carpenter's  wood  screws  (Fig.  33)  and  machinist's 
bolts  (Fig.  34).     Ordinarily,  however,  we  do  not  think  of  the 


FIG.  33.  —  Wood  screw. 


FIG.  34.  — Bolts. 


SIMPLE  MACHINES 


35 


O 


o 


FlG-  3r>-  ~  Screw 


FIG.  36.  —  Micrometer 
screw. 


propeller  of  a  boat  or  flying  machine  as  a  screw,  but  it  is.     The 

propeller  (Fig.  35),  with  its  two,  three,  or  four  blades  fas- 

tened to   one   end    of   the 

shaft,  is  driven  by  an  en- 

gine at  the  other  end.     Its 

rotation   is   so   rapid   that 

the  water  has  no  time  to 

get   out    of   the   way,   and    r\/-\ 

the  propeller  screws  itself 

through  the   water  like   a        O 

wood  screw  through  wood. 

Another  example  of  the  screw  is  the  micrometer  screw  (Fig. 

36),  which  is  used  to  make  very  precise  measurements.  It 
consists  of  an  accurately  turned  thread 
of  small  pitch,  perhaps  1  millimeter. 
It  is  evident  that  if  such  a  screw  is 
turned  ^^  of  a  complete  turn,  the 
spindle  moves  along  its  axis  just  0.01 
millimeters.  This  is  the  easiest  way 

of   measuring   so  small   a  distance.       In  order  to  discover 

readily  through  just  what  fraction  of  a  turn  the  screw  is 

turned,  the  head  is  divided  into  100  divisions. 
39.  Combinations  of 

simple  machines.     What 

is  called  a  single  machine 

in  factories  and  shops  is 

usually  a  combination  of 

the  simple  machine  ele- 

ments  described    above. 

It  is,  in  fact,  a  more  or 

less   complicated    collec- 

tion   of   levers,   pulleys, 

wheels,  axles,  and  screws. 

In  order  to  show  how  such 
a  machine   may  be  analyzed  FIG.  37.  —  Builder's  crane. 


36 


PRACTICAL   PHYSICS 


into  its  elements,  let  us,  as  it  were,  dissect  a  crane  or  derrick  (Fig.  37) 
such  as  is  used  in  unloading  freight  cars,  or  in  hoisting  building  material 
into  place. 

The  movable  pulley  to  which  W  is  attached  gives  a  mechanical  advan- 
tage of  two  ;  the  fixed  pulley  at  the  end  of  the  boom,  merely  changes  the 
direction  of  the  pull ;  the  wheel  D  and  its  axle  give  a  mechanical  advan- 
tage equal  to  the  ratio  of  the  size  of  the  wheel  to  the  size  of  the  axle. 
A  third  mechanical  advantage  is  gained  in  the  wheel  and  axle,  B  and  C, 
and  finally  there  is  the  mechanical  advantage  of  the  crank  P  and  the 
axle  A.  The  total  mechanical  advantage  of  this  compound  machine  is 
the  product  (not  the  sum)  of  the  separate  advantages  gained  by  its 
separate  elements.  This  is  true  of  compound  machines  in  general. 


PROBLEMS 

NOTE.    Friction  is  to  be  neglected  in  these  problems. 

1.  What  force  will  be  needed  to  pull  a  weight  of  200  pounds  slowly 
up  a  slope  which  rises  1  foot  in  25  feet  ? 

2.  What  weight   can  be  moved  on   a  10  %  grade  with  a  pull  of  50 
pounds  ? 

3.  A  boy,  who  <?an  push  with  a  force  of  80  pounds,  wants  to  roll  a 
200-pound  barrel  of  flour  into  a  cart  4  feet  above  the  ground.     How 
long  a  plank  will  he  need'? 

4.  What  force  is  needed  to  move  a  1500-pound  wagon  up  a  3  %  grade? 

5.  A  test  shows  that  it  takes  1000  pounds  more  force  to  haul  an  elec- 
tric car  weighing  4  tons  up  a  certain  grade  than  to  haul  it  along  on  a 

level.     What  is  the  grade  ? 

6.  What  weight  will  be   raised  by  a  jack- 
screw  when  a  force  of  40  pounds  is  applied  at 
the  end,of  a  lever  arm  2  feet  long,  the  pitch  of 
the  screw  being  0.3  inches  ? 

7.  In   a    letterpress    (Fig. 
38)  the  threads  are  0.25  inches 
apart  and  the  hand  wheel  is 
14  inches  in  diameter.     If  a 
15-pound    pull    is  applied    to 


FIG.  38. — Letterpress. 


the  rim  of  the  wheel,  how  much  force  is  brought  to 
bear  on  the  book? 

8.   The  pitch  of  the  screw  of  a  bench  vise  (Fig.  39) 
is  0.2  inches  and  the  handle  of  the  screw  is  7  inches  long. 
What  force  could  be  exerted  by  the  jaws  of  the  vise  if  a  force  of  25 
pounds  were  applied  at  the  end  of  the  handle  ? 


FIG.  39.  — Ma- 
chinist's vise. 


SIMPLE  MACHINES  37 

9.  The  lever  in  a  jackscrew  extends  2  feet  from  the  center.  If  a 
man  is  able  to  lift  25  tons  by  exerting  a  pressure  of  100  pounds,  how 
many  threads  to  the  inch  must  there  be  ? 

10.  In  the  preceding  problem,  what  is  the  mechanical  advantage? 

11.  In  the  crane  shown  in  figure  37,  the  weight  W  is  5  tons,  and  the 
radii  of  the  three  small  cogwheels  are  supposed  to  be  equal  and  each 
I  the  radius  of  the  crank  P  and  of  the  wheels  B  and  Z>,  which  are  also 
equal.     What  is  the  mechanical  advantage  of  the  whole  machine,  and 
what  force,  neglecting  friction,  must  be  applied  at  P  ? 

12.  The  pedal  of  a  bicycle  is  halfway  down  and  is  pressed  down 
with  a  force  of  100  pounds.     The  crank  arm  is  6  inches  long  and  the 
sprocket  wheel  is  8  inches  in  diameter.     Find  the  tension  or  pull  on  the 
chain. 

13.  In  the  preceding  problem  the  sprocket  wheel  attached  to  the  rear 
wheel  is  2.5  inches  in  diameter  and  the  wheel  is  28  inches  in  diameter. 
How  far  does  the  bicycle  go  when  the  pedal  makes  one  complete  revolu- 
tion ?     How  much  does  the  tire  of  the  rear  driving  wheel  push  backward 
on  the  roadbed  when  the  man  presses  100  pounds  on  the  pedal  ? 

40.  Work  and  power.    The  words  "  work  "  and  "  power  "  are 
often  confused  or  interchanged  in  colloquial  use.     The  term 
"work"  in  physics  means  the  overcoming  of  resistance.     For 
example,  if  a  boy  carries  a  pail  of  water  weighing  50  pounds 
up  a  flight  of  stairs  12  feet  high,  he  does  600  foot  pounds  of 
work.    The  amount  of  work  done  would  be  the  same  whether 
he  did  this  in  one  minute  or  one  hour,  but  the  amount  of 
power  required  to  do  this  job  in  one   minute  would  be  60 
times  the  power  required  to  do  it  in  one  hour.     The  term 
"power"  adds  the  notion  of  time.    Power  means  the  speed  or  rate 
of  doing  work. 

41.  Horse  power.     The  earliest  use  of  steam  engines  was 
to  pump  water  from  mines.     This  work  had  previously  been 
done  by  horses ;    so  the  power  of  the  various  engines  was 
estimated  as  equal  to  that  of  so  many  horses.     Finally,  James 
Watt  carried  out  some  experiments  to  determine  how  many 
foot  pounds  of  work  a  horse  could  do  in  one  minute.     He 
found  that  a  strong  dray  horse  working  for  a  short   time 
could  do  work  at  the  rate  of  33,000  foot  pounds  per  minute  or 


38 


PRACTICAL   PHYSICS 


550  foot  pounds  per  second.  This  rate  is  therefore  called  a 
horse  power.  To  get  the  horse  power  of  an  engine,  compute 
the  number  of  foot  pounds  of  work  done  per  minute  and  then 
divide  by  33,000,  or  per  second  and  divide  by  550. 


Horse  power  f  H  P  )  = 


nds  per  minute  _  foot  pounds  per  second 
33000  550 

Suppose  an  engine  is  used  to  'pump  10,000  gallons  of  water  per  hour 
into  a  reservoir  50  feet  above  the  supply.  How  much  horse  power  is 
required  ? 

One  gallon  of  water  weighs  8.34  pounds  ;  so  10,000  gallons  of  water 
weigh  83,400  pounds.  The  work  done  in  lifting  this  weight  50  feet  is 
83,400  x  50,  or  4,170,000,  foot  pounds.  Since  this  is  done  in  one  hour,  the 
work  per  minute  is  ^Vk0-00  or  69,500  foot  pounds.  The  horse  power 
required  would  be  fff££  or  2.1  H.  P. 

42.  Transmission  of  power.  In  any  shop  containing  sev- 
eral machines  one  easily  distinguishes  two  kinds  —  the  driv- 
ing machines,  which  may  be  steam,  gas  or  hot-air  engines,  or 
water  or  electric  motors,  and  the  driven  machines,  sucli  as 
lathes,  drills,  planers,  and  saws.  There  must  always  be  some 
connecting  link  between  a  driving  and  a  working  ma- 

chine ;  that  is,  some  means 
of  transmission.  If  these  ma- 
chines are  not  far  apart,  the 
common  method  is  to  use  shaft- 
ing, belts,  chains,  or  cogwheels; 
but  when  the  prime  mover  and 
the  driven  machine  are  widely 
separated,  sometimes  even 
miles  apart,  some  form  of  elec- 
trical  transmission  is  used. 
Electrical  transmission  will  be 
explained  later  in  Chapter 
XVIII. 

When  a  belt,  rope,  cable,  or 
endless  chain  is  used,  it  passes  over  two  pulleys,  as.  shown  in 
figure  40.  In  case  a,  the  pulleys  rotate  in  the  same  direction, 


FIG.  40.  —  Transmission  of  power  by  a 
belt. 


SIMPLE  MACHINES  39 

while  in  case  5,  where  the  belt  is  crossed,  they  rotate  in  op- 
posite directions.  It  is  evident  that  the  small  pulley  turns 
just  as  many  times  as  fast  as  the  large  pulley,  as  the  circum- 
ference (or  diameter)  of  the  small  pulley  is  contained  in  the 
circumference  (or  diameter)  of  the  large  pulley. 

The  same  is  true  of  cogwheels,  and  since  the  teeth  on  the 
perimeters  of  two  interlocking  wheels  must  be  the  same  size, 
it  follows  that  the  number  of  cogs  on  each  wheel  is  a  measure 
of  its  circumference.  The  speeds  of  two  such  wheels-  are  in- 
versely proportional  to  the  number  of  teeth  on  them.  Just 
as  in  the  case  of  two  pulleys  with  a  crossed  belt,  two  cog- 
wheels rotate  in  opposite  directions. 

Suppose  a  pulley  A  is  driving  a  second  pulley  B  by  means 
of  a  belt,  as  shown  by  the  arrows  in  figure  40 ;  both  sides  of 
the  belt  must  be  under  some  tension  in  order  to  give  the 
necessary  pressure  on  the  pulleys,  so  that  the  friction  may 
keep  the  belt  from  slipping.  It  is  the  usual  practice  to  drive 
with  the  upper  side  of  the  belt  slack,  so  that  any  sagging  due 
to  the  weight  of  the  belt  may  increase  the  arc  of  contact. 
The  tension,  then,  on  the  lower  side  (^)  must  be  greater 
than  the  tension  on  the  upper  side  (f).  It  is  the  difference 
in  tension  (T—i}  of  the  two  sides  of  the  belt  which  measures 
the  force  involved  in  the  transmission  of  power.  The  work 
done  in  one  minute  is  equal  to  the  difference  in  tension  times 
the  speed  of  the  belt  in  feet  per  minute. 

Horse  power  =  difference  in  tension  x  speed  (ft.  per  min.) 

33000 


PROBLEMS 

1.  If  it  takes  22  pounds  to  pull  a  200-pound  sled  along  a  level  road 
covered  with  snow,  how  much  work  is  done  in  dragging  the  sled  50  feet? 

•2.  In  the  preceding  problem,  if  the  sled  is  drawn  at  the  rate  of  4 
miles  an  hour,  how  many  horse  power  are  required? 

3.   How  much  work  can  a  5-horse-power  engine  do  in  10  minutes  ? 


40  PRACTICAL  PHYSICS 

4.  What  is  the  horse  power  of  an  elevator  motor,  if  it  can  raise  the 
car  with  its  load,  1500  pounds  in  all,  from  the  bottom  to  the  top  of  a 
100-foot  building  in  10  seconds  ? 

5.  An  aeroplane  with  a  50  horse-power  engine  makes  60  miles  an 
hour.     What  is  the  backward  thrust  of  the  propeller  ? 

6.  A  locomotive  pulling  a  train  along  a  level  track  at  the  rate  of 
25  miles  an  hour  expends  75  horse  power.     Find  the  total  resistance 
overcome. 

7.  A  motor  has  a  4-inch  pulley  which  is  belted  to  a  16-inch  pulley  on 
an  overhead  shaft.     The  motor  is  making  1800  revolutions  per  minute. 
What  is  the  speed  of  the  overhead  shaft  ? 

8.  In  an  electric  car  motor  a  pinion  or  small  cogwheel,  attached  to 
the  armature  shaft,  has  20  cogs,  and  the  gear  wheel  attached  to  the 
car  axle  has  36  cogs.     If  the  car  wheel  is  33  inches  in  diameter,  find 
the  number  of  revolutions   the  motor   makes  while  the  car  goes  100 
feet. 

9.  If  the  tension  T  in  the  tight  side  of  a  belt  1  inch  wide  can  safely 
be  44  pounds  greater  than  the  tension  t  in  the  slack  side  of  the  belt,  how 
fast  must  the  belt  run  to  transmit  1  horse  power? 

10.  It  takes  about  4  times  as  great  a  thrust  to  drive  an  aeroplane  at 
80  miles  an  hour,  as  to  drive  the  same  aeroplane  at  40  miles  an  hour. 
Compare  the  horse  powers  required  at  the  two  speeds. 

i 
43.    Friction.     In  the  study  of  machines  thus  far  we  have 

assumed  that  we  were  dealing  with  ideal  or  perfect  machines, 
in  which  the  output  equals  the  input.  But  in  every  actual 
machine  the  output  is  not  quite  equal  to  the  input.  This 
loss  or  waste  of  work  is  due  to  friction.  By  friction  we  mean 
the  resistance  which  opposes  every  effort  to  slide  or  roll  one  body 
over  another.  This  resistance,  which  always  opposes  the  mo- 
tion of  the  machine,  depends  on  the  condition  of  the  rubbing 
surfaces.  Great  pains  are  therefore  taken  to  diminish  the 
friction  as  much  as  possible  by  making  the  surfaces  which 
are  to  rub  together  smooth  and  hard,  and  by  using  various 
lubricants,  such  as  soap  and  paraffin  on  wood,  and  grease, 
oil,  and  graphite  on  metal.  For  example,  in  a  watch,  the 
hardened  steel  axles  turn  in  jewel  bearings,'  which  are  the 
hardest  and  smoothest  bearings  known,  and  are  lubricated 
with  a  special  oil  made  for  the  purpose. 


SIMPLE  MACHINES  41 

44.  So-called  laws  of  friction.     The  factors  which  control 
friction  in  any  actual  case  are  so  numerous  and  so  dependent 
upon  the  conditions,  that  only  the  most  general  principles  may 
be  stated  positively.      (1)  Experience  shows  that  starting 
friction  is  greater  than  sliding  friction.     For  when  we  push 
a  box  across  the  table,  we  find  that  the  force  necessary  to 
overcome  the  resistance  of  friction,  which  acts  like  a  back- 
ward drag,  is  greater  at  the  start  than  when  the  box  is  once 
in  motion.     (2)  Friction  does  not  much  depend  on  velocity, 
but  is  a  little  greater  at  slow  speeds.     (3)  Friction  depends 
very  much  on  the  nature  of  the  rubbing  surfaces.     (4)  When 
a  box  is  loaded,  it  requires  much  more  force  to  pull  it  along 
than  when  it  is  empty.     Careful  experiments  seem  to  show 
that  the  force  needed  to  slide  a  given  box  over  a  certain  floor 
is  just  about  doubled  when  the  pressure  (weight  of  box  and 
load)  is  doubled,  and  tripled  when  the  pressure  is  tripled. 
That  is,  the  force  needed  to  overcome  the  friction  seems  to 
be  proportional  to  the  pressure.     Experiments  show  that  this 
force  of  friction  may  be  a  very  small  fraction  of  the  pressure, 
such  as  0.06  in  the  case  of  lubricated  iron  on  bronze,  or  a 
large  fraction  of  the  pressure,  such  as  0.4  in  the  case  of  oak 
on  oak  without  lubricant. 

45.  Coefficient  of  friction.    This  fraction,  the  friction  divided 
by  the  pressure,  is  called  the  coefficient  of  friction. 

Coefficient  of  friction  =    force  of  friction 
pressure  or  weight 

In  accordance  with  the  statements  in  the  last  paragraph, 
the  coefficient  of  friction  for  any  particular  pair  of  surfaces 
is  pretty  nearly  constant  for  different  loads  or  speeds.  This 
is,  however,  only  an  approximation  to  the  truth.  Thus  it 
has  recently  been  found  that  the  coefficient  of  friction  of 
brake  shoes  on  railroad  car  wheels  nearly  doubles  when  the 
speed  drops  from  60  miles  an  hour  to  20  miles  an  hour. 
This  is  why  an  engineer  or  motorman  lessens  the  pressure  of 
his  brakes  as  his  train  or  car  slows  down. 


42  PRACTICAL  PHYSICS 

The  usefulness  of  even  roughly  accurate  coefficients  of 
friction  is  that  they  give  some  idea  of  how  much  resistance 
has  to  be  overcome  in  any  given  case.  Thus  in  the  country, 
farmers  often  haul  stones  and  pieces  of  heavy  machinery  on 
low  sledges  without  wheels,  called  stone  boats.  To  calcu- 
late how  much  force  is  needed  to  drag  such  a  stone  boat,  one 
has  only  to  look  up  the  coefficient  of  friction  between  wood 
and  dirt  (about  0.66)  in  an  engineer's  handbook,  and  multi- 
ply it  by  the  weight  of  the  boat  and  its  load.  For 

Force  of  friction  =  coefficient  of  friction  x  pressure. 

46.  Advantages  of  friction.  In  general  it  is  true  that 
friction  reduces  the  amount  of  useful  work  which  can  be 
gotten  out  of  a  machine,  yet  it  must  not  be  forgotten  that 
many  machines  depend  upon  friction  for  their  operation. 
Without  friction,  belts  would  not  cling  to  their  pulleys, 
ropes  could  not  be  made,  nails  and  screws  would  be  useless, 
and  even  walking  would  be  impossible,  as  any  one  can  see 
who  has  experienced  the  difficulty  of  running  on  a  polished 
floor  or  on  ice.  It  is  friction  which  has  made  possible  our 
high-speed  express  trains ;  first  because  it  is  the  friction  or 
traction  between  the  driving  wheels  of  the  locomotive  and 
the  rails  that  enables  them  to  move  at  all,  and  second,  because 
it  is  the  friction  between  the  brakes  and  the  car  wheels  that 

enables  them  to  stop  quickly 
in  case  of  emergency. 

47.  Rolling  friction. 
Every  one  knows  that  the 
friction  which  opposes  drag- 
ging a  load  along  can  be 
greatly  reduced  by  mount- 

FIG.  41.  — Rolling  friction  (exaggerated).  J  J        ,        . 

ing  the  load  on  wheels,  but  it 

should  be  noticed  that  even  in  this  case  there  is  something 
equivalent  to  friction  between  the  wheels  and  the  roadbed. 
When  a  car  wheel  rolls  over  a  smooth  track,  as  shown  in 


SIMPLE  MACHINES  43 

figure  41,  its  own  weight  and  that  of  its  load  flatten  it  a  little 
where  it  rests  on  the  track,  and  also  make  a  slight  depression 
in  the  track.  So  as  it  rolls  along  it  is  continually  forced  to 
climb  up  out  of  the  depression.  Of  course  this  depression  is 
not  easy  to  detect  in  the  case  of  a  steel  track,  but  in  the  case 
of  a  soft  dirt  road  it  is  very  considerable.  It  is  for  this 
reason  that  the  wheels  of  wagons  which  carry  heavy 
loads  are  provided  with  wide  tires  so  as  to  sink  less 
into  the  roadbed  ;  and  for  just  this  reason  the  hard  sur- 
faces of  car  wheels  and  tracks  enable  a  locomotive  to  pull 
enormous  loads.  This  resistance  to  rolling  is  called  rolling 
friction. 

The  great  advantage  of  ball  and  roller  bearings  is  that 
they  substitute  rolling  for  sliding  friction  between  the  axles 
and  their  bearings.  But  even  in  ball  bearings  there  is 
some  sliding  friction  where  adjoining  balls  rub  against  each 
other. 

48.  Efficiency  of  machines.  The  efficiency  of  a  machine 
is  the  ratio  of  output  to  input.  It  is  usually  expressed  as  a 
per  cent;  that  is,  the  output  is  a  certain  per  cent  of  the  input 
delivered  to  the  machine. 

•!?.«„:«„          output     work  done  by  machine 
Efficiency  =  —     —  =  -  —  •*—    -—  —  » 

input      work  done  on  machine 

or  Output  =  efficiency  x  input. 

For  example,  suppose  we  have  an  inclined  plane  of  5  %  grade  (5  feet 
rise  in  100  feet)  and  a  load  of  one  ton.  If,  because  of  friction,  it  takes  a 
pull  of  150  pounds  to  haul  the  load  up  the  slope,  what  is  the  efficiency? 
In  lifting  2000  pounds  5  feet,  we  do  10,000  foot  pounds  of  work  ;  this  is 
the  output.  But  we  must  pull  with  a  force  of  150  pounds  through  100 
feet,  or  put  in  15,000  foot  pounds  of  work.  Therefore  the  efficiency  is 

,  or  0.667,  or  66.7%. 


The  efficiency  of  a  lever  where  the  friction  is  very  small  is  nearly 
100  %,  but  in  the  commercial  block  and  tackle  it  is  sometimes  less  than 
50%,  and  in  the  jackscrew,  the  friction  is  so  large  that  the  efficiency  is 
often  as  low  as  25  %. 


44  PRACTICAL  PHYSICS 


PROBLEMS 

1.  A  tool  is  pressed  on  a  grindstone  with  a  force  of  25  pounds ;  the 
coefficient  of  friction  is  0.3.     What  is  the  backward  pull  of  friction? 

2.  The  coefficient  of  friction  between  the  driving  wheels  of  a  loco- 
motive and  the  rails  is  0.25.     How  much  must  the  locomotive  weigh  in 
order  to  exert  a  pull  of  10  tons  ? 

3.  A  test  shows  that  it  takes  a  pull  of  17  pounds  to  pull  on  ice  a  man 
weighing  150  pounds.     What  is  the  coefficient  of  friction  ? 

4.  In  lifting  a  1250-pound  block  of  marble  to  a  height  of  90  feet,  the 
hoisting  engine  did  125,000  foot  pounds  of  work.     What  was  the  efficiency 
of  the  hoist  ? 

5.  What  load  can  a  pair  of  horses,  working  at  the  rate  of  2  horse 
power,  draw  along  a  level  highway  at  the  rate  of  3  miles  an  hour,  if  the 
coefficient  of  friction  of  the  wagon  on  the  road  is  0.17? 

6.  With  a  certain  block  and  tackle  it  is  found  that  a  force  of  125 
pounds  is  necessary  to  lift  a  weight  of  500  pounds,  and  the  force  must 
move  6  feet  in  order  to  raise  the  weight  1  foot.     What  is  the  efficiency 
of  this  block  and  tackle? 

7.  A  motor  whose  efficiency  is  90%  delivers  5  horse  power.     What 
must  be  the  input  ? 

8.  A  hod  carrier,  weighing  160  pounds,  carries  100  pounds  of  brick 
up  a  ladder  to  a  height  of  35  feet.     How  much  work  does  he  do  in  all? 
How  much  of  it  is  useful  work  ? 

9.  What  is  the  efficiency  of  a  pump  which  can  deliver  250  cubic  feet 
of  water  per  minute  to  a  height  of  20  feet,  if  it  takes  a  10  horse-power 
engine  to  run  it? 

10.  A  steam  shovel  driven  by  a  6  horse-power  engine  lifts  200  tons  of 
gravel  to  a  height  of  15  feet  in  an  hour.  How  much  work  is  done  against 
friction  ? 


SUMMARY   OF   PRINCIPLES   IN    CHAPTER   II 

The  principle  of  moments:   used  in  solving  all  kinds  of  levers, 
straight  and  bent,  the  wheel  and  axle,  etc. ;  — 

Effort  x  lever  arm  =  resistance  x  lever  arm. 

To  get  force  on  fulcrum :    or  to  solve  a  pulley  system, 
Sum  of  forces  up  =  sum  of  forces  down. 


SIMPLE  MACHINES  45 

Laws  of  equilibrium:    applicable  to  any  object  at  rest  under  the 
action  of  two  or  more  forces ;  — 

(1)  Sum  of  forces  in  any  direction 

=  sum  of  forces  in  opposite  direction. 

(2)  Sum  of  moments  clockwise  around  any  point 

=  sum  of  moments  counter-clockwise  around  same 
point. 

The  principle  of  work;  — 

Work  (foot  pounds)  =  force  (pounds)  x  distance  (feet). 

In  any  frictionless  machine, 

Input  =  output. 
If  there  is  friction, 

Input  =  output  4-  work  lost  by  friction. 

Power  =  rate  of  doing  work. 

i  horse  power  =  550  foot  pounds  per  second, 

=  33,000  foot  pounds  per  minute. 

Coefficient  of  friction  =  force  of  friction . 

pressure 

Force  of  friction  =  coefficient  x  pressure. 
Efficiency  =° 


input 

Output  =  efficiency  x  input. 

QUESTIONS 

1.  Make  a  list  of   a  dozen  applications  of  the  simple  machine  ele- 
ments described  in  this  chapter  that  you  have  seen  outside  of  the  class- 
room within  a  week. 

2.  Distinguish  between  the  popular  use  of  the  term  "work"  and  its 
technical  use  in  physics  and  engineering.     Give  an  example  of  "  work  " 
that  is  not  technically  "work." 

3.  Analyze  the  working  of  the  following  machines  :    clothes  wringer, 
broom,  ice-cream  freezer,  plow,  grindstone,  and  rotary  meat  chopper. 


46 


PRACTICAL   PHYSICS 


4.  Distinguish   between    the   terms   "  mechanical   advantage "  and 
"efficiency."     Illustrate  by  an  example. 

5.  Is  there  any  "  mechanical  advantage "  in  an  equal  arm  lever  ? 
Why  is  it  often  used  in  machines? 

6.  Why  is  an  unequal  arm  lever  useful? 

7.  Show  how  the  principle  of  work  applies  to  the  lever. 

8.  How  would  you  calculate  the  moment  of  the 
force  F  as  applied  to  the  grindstone  in  figure  42  ? 

9.  Why  are  you  likely  to  twist  off  the  head  of  a 
screw  by  using  a  screwdriver  in  a  bit  brace  ? 

10.  When  a  machinist  speaks  of  "  an  8-32  screw/' 
what  does  he  mean  ? 

11.  What  is  meant  by  a  perpetual -motion  ma- 
chine ? 

12.  -What  kind  of  lubricant  is  used  on  journals  of 
car  wheels?     What  kind  on  clocks  and  watches? 
Why  the  difference  in  kind  of  lubricant? 

13.  What  determines  the  "angle  of  repose,"  or 
slope,  of  the  rock  waste,  or  talus,  at  the  base  of  a  cliff? 

14.   Why  are  the  modern  air  brakes  on  cars  more  effective  than  the 
old-fashioned  hand  brakes  ? 


FIG.  42. —Crank 
grindstone. 


CHAPTER   III 


MECHANICS   OF   LIQUIDS 

Hydraulic  machines  —  Pascal's  principle  of  transmitted  pres- 
sure—  applications  in  presses  and  elevators  —  pressure  in  a 
liquid  due  to  its  weight  —  levels  of  liquids  in  connecting  vessels 
—  upward  pressure  of  liquids  —  Archimedes'  principle  and  its 
applications  —  specific  gravity  of  solids  and  liquids  —  city  water 
works,  faucets,  gauges,  and  meters  —  water  wheels  —  interaction 
between  solids  and  liquids  —  capillarity. 

49.  Hydraulic  machines.  As  we  continue  our  study  of 
machines  we  find  some  machines  that  involve  more  than  the 
simple  elements,  the  lever,  the  pulley,  and  the  screw.  For 
instance,  there  are  a  great  many  machines  that  make  use  of 
liquids,  such  as  the  water  wheel,  hydraulic  press,  and 
hydraulic  elevator.  These  are  called  hydraulic  machines, 
and  this  chapter  will  be  devoted  to  the 
study  of  them.  In  the  course  of  it  we 
shall  also  have  to  consider  dams  and  reser- 
voirs, as  well  as  all  sorts  of  things  that 
float  or  sink  in  water. 


50.   Pressure   transmitted   by   a    liquid. 

Suppose  we  fill  a  bottle  with  water  and  close  it 
with  a  one-hole  rubber  stopper.  Then  let  us  fasten 
the  stopper  securely,  as  shown  in  figure  43,  and 
force  into  the  hole  a  metal  rod  of  such  a  size  as  to 
fit  rather  tightly.  The  force  applied  to  the  rod 
will  be  transmitted  to  the  inner  surface  of  the 
bottle,  and  the  bottle  will  burst. 


This  experiment  shows  that  the  water    FIG  43. -Water trans- 
mits pressure  of  pis- 
which  is  pressing  against  the  bottom  of       ton. 

47 


48 


PRACTICAL  PHYSICS 


the  piston   is   also    pressing    against   everything   else   that 

it  touches. 

51.    Pascal's  principle.     It   seems    reasonable   to   suppose 

that  if  we   had  a   box  filled   with   water  and   fitted    with 

two  equal  pistons  A  and  B,  as 
in  figure  44,  the  water  would 
press  equally  hard  on  each  pis- 
ton. It  is  also  evident  that  if 
a  third  equal  piston  were  placed 
in  the  side  of  the  box,  as  at  (7, 
the  water  would  press  sideways 
on  it  with  an  equal  force.*  In 
short,  if  a  liquid  is  pressing 
against  any  square  inch  with  a 


FIG.  44.  —  Pascal's  principle. 


certain  force,  it  is  pressing  equally  hard  against  every  square 
inch  of  everything  it  touches. 

52.  The  hydraulic  press.  The  most  useful  application  of 
this  principle  can  be  described  in  Pascal's  (1623-1662)  own 
words :  "  If  a  vessel  full  of  water,  closed  in  all  parts,  has 
two  openings,  of  which  the  one  is  a  hundred  times  the  other, 
placing  in  each  a  piston  which  fits  it,  the  man  pushing  the 
small  piston  will  equal  the  force  of  a  hundred  men  who  push 
that  which  is  a  hundred  times  as  large,  and  surpass  that  of 
ninetjr-nine.  Whatever  proportion  these  openings  have,  and 
whatever  direction  the 
pistons  have,  if  the  forces 

that  apply  on  the  pistons   sg."*n  ^^^^^^  H3 1  s«  in< 

are  as  the  openings,  they 
will  be  in  equilibrium." 


100 


100  Ibs. 

uumumi 

1  Ib 

m 

M^^P^^i^ 

^r-_-^^-_^^- 

^ 

=^-=~-  ~E^-=:  ^7^-Z^ 

-^I^-Z^T^EI^ 

FIG.  45.  —  Diagram  of  hydraulic  press. 


This  refers  to  a  mechanism 
like  that  shown  in  figure  45. 
Suppose  there  is  a  force  of 

one  pound  pushing  down  on  the  small  piston,  and  that  the  large  piston 
has  100  times  as  great  an  area.  Then  there  must  be  100  pounds  push- 
ing down  on  the  large  piston  to  balance  it.  It  will  be  seen,  however, 

*  The  effect  of  the  weight  of  the  liquid  is  here  neglected. 


BLAISE  PASCAL.  French  scientist  and  mathematician.  Born  1623.  Died  1662. 
Studied  the  pressures  exerted  by  liquids  and  gases.  Famous  also  for  his  achieve- 
ments in  mathematics. 


MECHANICS   OF  LIQUIDS 


49 


that  the  pressure  on  each  square  inch  of  the  large  piston  is  one  pound. 
In  other  words  the  pressure  has  been  transmitted  by  the  liquid  so  as  to 
act  with  the  same  force  on  every  square  inch. 

53.  Applications  of  the  hydraulic  press.  This  device  of 
Pascal  gives  us  an  easy  way  of  exerting  enormous  forces, 
such  as  are  needed  in  baling  paper,  cotton,  etc.,  in  punching 
holes  through  steel  plates,  and  for  extracting  oil  out  of  seeds. 
The  commercial  machine  (Fig. 
46)  is  exactly  like  that  described 
by  Pascal  except  that  there  is 
usually  a  check  valve  (v)  between 
the  small  piston  and  the  big  one, 
and  the  small  piston  is  arranged 
to  work  like  a  pump,  with  a 
valve  (d)  at  the  bottom  for  admit- 
ting more  oil.  Often  the  small 
piston  is  forced  down  by  a  lever. 
The  method  of  operation  is  sim- 
ple. On  the  upstroke  of  the 
pump  piston,  the  valve  at  the 


FIG.  46.  —  Hydraulic  press. 


bottom  of  the  pump  opens  and  oil  flows  in  from  the  reser- 
voir. On  the  downstroke  of  the  pump  piston,  the  oil  is 
forced  over  through  the  connecting  pipe  past  the  valve,  and 
pushes  the  large  working  piston  up  very  slightly.  If  the 
large  piston  is  100  times  as  large  in  cross  section  as  the 
small  piston  (i.e.  diameters  as  10  : 1),  the  large  piston  is 
lifted  only  -^^  the  distance  the  pump  piston  is  pushed  down 
each  stroke.  But  since  the  force  exerted  by  the  large  piston 
is,  neglecting  friction,  100  times  that  applied  to  the  small 
piston,  it  follows  that  the  work  done  on  the  machine  is  equal 
to  the  work  done  by  the  machine.  If  we  consider  the  work 
done  against  friction,  the  equation  becomes,  — • 

Input  =  output  +  work  done  against  friction. 

54.  Working  model  of  a  hydraulic  press.    Let  us  try  to  appreciate 
the  tremendous  forces  which  are  obtainable  with  the  hydraulic  press  by 


50 


PRACTICAL  PHYSICS 


operating  a  model  press,  such  as  is  shown  in  figure  47,  to  break  a  stick 
of  wood.  By  measuring  the  diameters  of  the  pistons,  and  the  lengths 
of  the  lever  arms,  we  may  calculate  the  total  mechanical  advantage  of 
the  machine. 


FIG.    47.— Working    model   of       FIG.  48.  —  Hydrostatic 
hydraulic  press.  bellows. 

Another  striking  experiment  is  to  let  a  boy  bal- 
ance his  own  weight  against  a  column  of  water  by 
means  of  the  hydrostatic  bellows  (Fig.  48).  By  cal- 
culating the  actual  areas  involved  and  the  force 
acting  on  each  square  inch,  we  may  compute  the 
height  of  water  that  should  be  required  and  compare 
this  with  the  actual  height. 

55.  Hydraulic  elevators.  Pascal's  prin- 
ciple is  also  used  in  hydraulic  elevators, 
which  are  commonly  employed  where  heavy 
machinery  is  to  be  lifted.  A  simple  form 
is  shown  in  figure  49.  At  the  bottom  of 
the  elevator  well  is  a  pit  as  deep  as  the  building  is  high. 
In  the  pit  is  a  cylinder  ( (7)  and  in  this  C}^linder  is  a  plunger 
(P),  to  the  top  of  which  the  elevator  cage  (^4)  is  firmly 
fastened.  When  water  under  pressure  (often  simply  the 
pressure  of  the  water  mains)  is  admitted  through  the  valve 
(v)  into  the  cylinder,  the  plunger  rises  and  forces  up  the 
elevator.  The  weight  of  the  elevator  is  partly  counter- 


FIG.  49.— Hydraulic 
elevator. 


MECHANICS   OF  LIQUIDS  51 

balanced  by  a  weight  (IF).  When  the  operator,  by  pulling 
the  cord,  turns  the  valve  so  as  to  connect  the  cylinder  in 
the  pit  with  the  sewer  pipe,  the  elevator  comes  down. 

When  speed  is  demanded,  as  in  high  office  buildings,  the 
motion  of  the  hydraulic  plunger  is  communicated  to  the 
cage  by  a  cable  passing  over  a  series  of  pulleys,  so  that 
the  cage  moves  four  times  as  far  and  four  times  as  fast  as 
the  plunger. 

56.  Pressure  and  force.  It  is  necessary  to  distinguish  be- 
tween the  terms  pressure  and  force.  Force  means  a  push  or  a 
pull,  and  is  usually  expressed  in  terms  of  the  push  or  pull 
necessary  to  hold  up  a  given  weight,  such  as  a  pound  or 
a  kilogram.  Pressure  means  the  push  or  pull  per  unit  area 
of  surf  ace.  Pressure  may  be  expressed  in  various  ways,  for 
example,  as  so  many  grams  per  square  centimeter  or  so  many 
pounds  per  square  inch. 

The  real  advantage  of  the  hydraulic  press  is  that,  although 
the  pressure  on  the  large  piston  is  exactly  the  same  as  that 
on  the  small  piston,  the  force  exerted  by  the  large  piston  is 
many  times  greater. 

PROBLEMS 

1.  If  the  diameters  of  two  pistons  in  a  hydraulic  press  are  1  inch  and 
10  inches,  what  are  their  areas  of  cross  section  ? 

2.  If   the  small  piston   in   problem   1  is  subjected  to  a  pressure  of 
10  pounds  per  square  inch,  what  pressure,  neglecting  friction,  must  be 
applied  to  the  large  piston  to  hold  it  in  place  ? 

3.  If  a  total  force  of  10  pounds  is  applied  to  the  small  piston  in  prob- 
lem 1,  what  total  force  must  be  applied  to  the  large  piston  to  hold  it 
in  place  ? 

4.  The  diameters  of  the  pistons  in  a  hydraulic  press  are  20  inches  and 
1  inch.     What  must  be  the  force  on  the  small  piston  if  a  force  of  5  tons  is 
to  be  exerted  by  the  large  piston? 

5.  In  problem  4,  suppose  the  small  piston  to  move  1  foot.     How  far 
does  the  large  piston  move  ? 

6.  If  the  water  pressure  in  a  city  water  main  is  50  pounds  per  square 
inch  and  the  diameter  of  the  plunger  of  an  elevator  is  10  inches,  how 
heavy  a  load  can  the  elevator  lift  ?    If  the  friction  loss  is  25  %,  what 
load  can  be  lifted  ? 


52  PRACTICAL  PHYSICS 

57.  Pressure  in  a  liquid  due  to  its  weight.     Not  only  does 
a  liquid  transmit  pressure  when  it  is  in  a  closed  vessel,  but  a 
liquid  in  an  open  vessel,  such  as  water  in  a  tin  pail,  exerts  a 
pressure  on  the  bottom  of  the  vessel  because  the  liquid  is  it- 
self heavy.     This  bottom  pressure,  that  is,  the  force  on  each 
square  inch,  evidently  depends  on  the  depth  of  the  liquid,  and 
also  on  its  density. 

For  example,  suppose  we  have  a  box  with  a  bottom  10  centimeters  by 
20  centimeters  and  15  centimeters  deep,  filled  with  water.  Then  on 
each  square  centimeter  of  the  bottom  of  the  box  there  rests  a  column  of 
water  15  centimeters  tall,  weighing  15  grams,  and  so  the  pressure  on  the 
bottom  is  15  grams  per  square  centimeter.  The  total  downward  force  of 
the  water  against  the  bottom  would  be  200  x  15,  or  3000  grams,  for 

Total  force  =  area  x  pressure. 

If  the  box  were  filled  with  mercury  instead  of  water,  the  pressure  on  the 
bottom  would  be  the  weight  of  a  column  of  mercury  15  centimeters  high 
and  1  square  centimeter  at  the  base;  that  is,  the  weight  of  15  cubic 
centimeters  of  mercury.  Since  1  cubic  centimeter  of  mercury  weighs 
13.6  grams,  15  cubic  centimeters  would  weigh  15  x  13.6,  or  204  grams. 
The  total  force  of  the  mercury  pushing  down  on  the  bottom  of  the  box 
would  be  200  x  204,  or  40,800  grams,  or  40.8  kilograms. 

58.  Bottom  pressure  and  shape  of  vessel.     So  far  we  have 
considered  vessels  with  vertical  sides  such  as  A  in  figure  50. 


d 
C 
FIG.  50.  — Vessels  with  (A)  vertical,  (B)  flaring,  and  (C)  conical  sides. 

In  the  ordinary  pail,  however,  the  sides  are  not  vertical,  but 
flare  outward  as  shown  in  B  in  figure  50.  Perhaps  one 
might  expect  that  the  pressure  on  each  square  centimeter  of 
the  bottom  would  be  greater  than  in  case  J.,  because  there  is 
so  much  more  water  in  the  vessel.  This,  however,  is  not 
the  case.  Each  square  centimeter  of  the  bottom  has  to  hold 


MECHANICS   OF  LIQUIDS 


53 


up  only  the  little  column  of  water  above  it  just  as  it  did  in 
case  A.  The  extra  water  above  the  slanting  sides  is  held  up 
by  those  sides  and  not  by  the  bottom.  If  the  area  of  the 
base  and  depth  of  liquid  is  the  same  in  both  A  and  B,  then 
the  total  downward  push  of  the  liquid  on  the  bottom  will  be 
the  same  even  though  B  holds  more  liquid  than  A. 

In  case  (7,  the  depth  of  liquid  and  area  of  base  are  the 
same  as  in  cases  A  and  J9,  but  the  top  is  smaller  than  the 
base.  It  is  easy  to  see  that  the  pressure  on  that  portion  of 
the  base  ab  directly  under  the  top  would  be  the  same  as  in 
the  other  vessels,  but  it  might  at  first  seem  that  the  pressure 
would  gradually  decrease  as  we  go  from  a  to  c  and  from  I  to 
d.  There  is  an  interesting  experiment  devised  to  settle  this 
question. 

59  Experiments  with  Pascal's  vases.  The  apparatus  (Fig.  51) 
consists  of  three  glass  vessels  of  shapes  to  correspond  roughly  to  A,  B, 
and  C  in  figure  50.  The  bottom 
of  each  vessel  is  made  the  same 
size  and  screws  into  a  short  cyl- 
inder, across  the  bottom  of  which 
is  tied  a  disk  of  sheet  rubber. 
The  pointer  below  is  a  lever  with 
its  short  arm  pressing  against  the 
center  of  the  rubber  disk,  and 
the  long  arm  moves  up  and  down 
across  a  scale. 

With  this  apparatus  it  is 
possible  to  show  that  (a)  the 
downward  pressure  of  a  liquid 
is  proportional  to  the  depth, 
(b)  the  downward  pressure  of  a  liquid  is  proportional  to  its 
density,  and  (c)  the  downward  pressure  in  a  liquid  is  inde- 
pendent of  the  shape  of  the  vessel. 

It  seems  impossible  that  unequal  quantities  of  water 
should  exert  an  equal  downward  push  against  the  bottom. 
But  if  we  recall  that  when  the  sides  slope  outward,  the  sides 


FIG.  51.  —  Pascal's  vases. 


54 


PRACTICAL  PHYSICS 


hold  up  the  excess  of  water,  we  can  see  that  when  the  sides 
slope  inward,  they  push  down  enough  to  make  up  for  the 
deficit  in  water. 

60.  Liquids  also  exert  pressure  sidewise.     We  all  know 
that  if  a  hole  is  bored  in  the  side  of  a  tank  or  barrel  of  water, 
the  water  will  spurt  out.     This  means  that  before  the  hole 
was  bored  the  liquid  must  have  been  pressing  against  that  bit 

of  the  side  of  the  barrel.  Liquids,  then, 
exert  a  sidewise  pressure  due  to  their 
weight,  as  well  as  a  downward  pressure. 

We  can  investigate  how  this  sidewise  pres- 
sure varies  with  the  depth  and  .the  direction 
by  means  of  the  gauge  shown  in  figure  52. 
The  apparatus  consists  of  a  rubber  diaphragm, 
which  may  be  turned  about  a  horizontal  axis, 
and  is  connected  by  a  rubber  tube  to  a  hori- 
zontal glass  tube  containing  a  globule  of  some 
colored  liquid.  As  we  lower  the  pressure  gauge 
into  the  jar  of  water,  we  observe  that  the  globule 
moves  to  the  right  showing  a  gradual  increase  of 
pressure  with  increase  of  depth.  If  we  repeat 
this  with  the  diaphragm  facing  in  another  direc- 
FIG.  52. -Pressure  gauge  tion>  we  get  the  same  resulL  If  we  hold  the 
to  show  pressure  equal  frame  ftt  gome  fixed  d  th  and  rotate  the  dia_ 

in  all  directions.  ' 

phragrn  around  a  horizontal  axis,  we  find  the 

globule  remains  practically  stationary,  showing  that  the  pressure  is  the 
same  in  all  directions. 

The  sidewise  pressure  of  a  liquid  increases  with  the  depth  and 
density  of  the  liquid.  At  a  given  depth  a  liquid  presses  down- 
ward and  sidewise  with  exactly  the  same  force. 

61.  Calculation  of  sidewise   pressure.    '  To   calculate  the 
sidewise  push  of  water  against  a  dike  or  dam,  we  have  to 
remember  that  both   the  downward  and  sidewise   pressure 
increase  gradually  from  zero  at  the  surface  to  their  value  at 
the  bottom.     We  have  already  seen  that  this  bottom  pressure 
is  equal  to  the  weight  of  a  column  of  water  with  a  base  one 
unit  square  and  with  a  height  equal  to  the   depth.     The 


MECHANICS   OF  LIQUIDS 


55 


average  side  wise  pressure  is  equal  to  the  pressure  halfway 
down,  or  is  one  half  the  bottom  pressure.  The  total  side- 
wise  push  of  the  water  against  the  dam  is  then  equal  to  the 
area  times  the  average  pressure. 

For  example,  suppose  we  have  a  box  10  centimeters  wide,  20  centi- 
meters long,  and  15  centimeters  deep  filled  with  water.  What  is  the 
total  force  tending  to  push  out  the  end  of  the  box  ?  The  pressure  at  a 
point  halfway  down  the  side  would 
be  7.5  grams  per  square  centimeter. 
There  are  in  the  end  10  x  15,  or  150 
square  centimeters.  Therefore  the 
total  force  against  the  end  is  150  x 
7.5,  or  1125  grams. 

Again,  suppose  the  box  were  a 
large  tank  full  of  water,  and  the  di- 
mensions, expressed  in  feet,  were  10 
by  20  by  15.  What  is  the  end  thrust? 
The  pressure  halfway  down  would  be 
the  weight  of  a  column  of  water  with 


FIG. 


15  cm 


20  cm 

53.  —  Sidewise    push    of    water 
against  end  of  box. 


1  square  foot  for  its  base  and  7.5  feet  high,  i.e.  7.5  x  62.4,  or  468  pounds  per 
square  foot.  Since  there  are  10  x  15,  or  150  square  feet,  in  the  end  of  the 
tank,  the  total  end  thrust  is  150  x  468,  or  70,200  pounds,  or  about  35  tons. 

62.    Levels  of  liquids  in  connecting  vessels.     Probably  every 
one  has  observed  that  water  stands  at  the  same  level  in  the 

spout  of  a  teakettle  as  in  the 
kettle  itself  (Fig.  54).  In  other 
words,  liquids  seek  their  own  level, 
or  the  same  liquid  in  any  number 
of  connecting  vessels  will  have 
its  free  surface  at  the  same  level 
in  each.  This  is  to  be  expected 
from  the  fact  that  the  pressure  in 
a  liquid  depends  upon  the  depth 
FIG.  M. -water  seeks  its  own  below  the  free  surface.  Thus  if 

level  in  a  teakettle.  •.•-..! 

any  point  in  the  connecting  por- 
tion between  the  two  vessels  were  unequally  far  below  the 
two  surfaces,  the  pressures  in  either  direction  would  not 


56 


PRACTICAL  PHYSICS 


balance,  and  the  liquid  would  flow  from  one  vessel  to  the 

other  until  the  levels  were  equalized. 

The  water  gauge  on  a  steam  boiler  (Fig.  55)  is  a  good 
application  of  this  principle.  The 
gauge  consists  of  a  thick-walled  glass 
tube  which  connects  at  the  top  with  the 
steam  space,  and  at  the  bottom  with  the 
water  in  the  boiler.  The  valves  A.  and 
B  are  closed  when  the  glass  tube  is  to 
be  replaced.  The  valve  C  is  opened  oc- 
casionally to  test  the  gauge  to  see  that  it 
reads  correctly  and  has  not  clogged  up. 
63.  Upward  pressure  of  liquids.  If 
one  tries  to  push  a  pail  under  water 
bottom  downward,  he  finds  he  must 
overcome  considerable  resistance  because 

FIG'  "'"iblriter  gauge°n  of  the  upward  push  of  the  water  on  the 
pail.     In  order  to  see  just  how  much 

this  upward  push  of  the  water  is,  let  us  try  the  following 
experiment. 

Let  a  glass  cylinder,  which  has  its  bottom  edge  ground  off  smooth, 
be  closed  with  a  glass  plate  or  piece  of  cardboard,  held  in  place  by  a 
thread,  as  shown  in  figure  56.  When  we 
push  this  cylinder  into  a  jar  of  water,  we 
can  let  go  the  thread  and  yet  the  glass 
bottom  will  not  fall  off.  It  is  evident 
that  there  is  an  upward  pressure  due  to 
the  water,  and  the  next  question  is,  how 
much?  If  we  pour  colored  water  into 
the  cylinder  until  the  bottom  drops 
off,  we  shall  have  to  fill  the  cylinder 
until  the  levels  inside  and  outside  are 
the  same. 


In  general  we  may  say  that  the 
upward  pressure  exerted  by  a  liquid 
at  any  depth  is  equal  to  the  down- 


(j>  —  Upward  pressure  oi 

water. 


MECHANICS  OF  LIQUIDS  57 

ward  pressure  which  would  be  exerted  by  the  same  liquid  at 
the  same  depth. 

PROBLEMS 

1.  The  water  in  a  standpipe  is  10  meters  deep.     What  is  the  pres- 
sure on  one  square  centimeter  of  the  bottom  ? 

2.  The  water  in  a  standpipe  is  40  feet  deep.     What  is  the  pressure 
on  one  square  inch  of  the  bottom  ? 

3.  If  the  diameter  of  the  tank  in  problem  2  is  10  feet,  what  is  the 
total  force  which  the  bottom  of  the  tank  must  sustain  ? 

4.  A  diver  goes  down  into  sea  water  (density  1.03  grams  per  cubic 
centimeter)  to  a  depth  of  10  meters.     What  is  the  pressure  on  him  in 
kilograms  per  square  centimeter? 

5.  The  hydraulic  engineer  speaks  of  pressure  as  "head  of  water," 
which  means  the  pressure  due  to  the  weight  of  column  of  water  as  high 
as  the  "  head  of  water."     Express  in  pounds  per  square  inch  a  "  head  of 
50  feet." 

6.  What  is  the  pressure,  near  the  keel,  on  a  vessel  drawing  6  meters? 

7.  Figure   57   is   a  cylindrical  tank   10  x  12  centi- 
meters ;  out  of  the  top  rises  a  tube  20  centimeters  long. 
The  box  and  tube  are  filled  with  water. 

(a)  Find  the  pressure  in  grams  per  square  centimeter 

at  the  bottom  of  the  tank. 
(6)  Does  the  size  of  the  tube  affect  the  pressure  on  the 

bottom  ? 

(c)  Find  the  pressure  halfway  up  the  side  of  the  tank. 

(d)  Find  the  pressure  at  the  top  of  the  tank. 

8.  A  rectangular  tank  is  5  feet  wide,  10  feet  long, 
and  4  feet  deep.     Calculate  the  total  force  exerted  on 
the  end  when  the  tank  is  full  of  water. 


<— 12  cm. 

9.  Assuming  that  a  cubic  inch  of  mercury  weighs  FIG.  57.  —  Box 
0.49  pounds,  find  the  pressure  on  the  bottom  of  a  turn-  and  tube  full 
bier  in  which  the  mercury  stands  4  inches  deep.  of  water. 

10.  How  high  a  column  of  water  could  be  supported  by  a  pressure  of 
one  kilogram  per  square  centimeter? 

11.  If  the  density  of  mercury  is  13.6  grams  per  cubic  centimeter,  what 
is  the  pressure  exerted  at  the  base  of  a  column  76  centimeters  high  ? 

12.  A  dam  is  50  feet  long  and  6  feet  high,  and  the  water  just  reaches 
the  top.     What  is  the  total  force  against  the  dam  ? 

13.  A  hole  6  inches  square  is  cut  in  the  bottom  of  a  ship  drawing  18 
feet  of   water.     What  force  must  be  exerted  to  hold  a  board  tightly 
against  the  inside  of  the  hole  ? 


58 


PRACTICAL  PHYSICS 


14.  How  much  "  head  of  water  "  is  needed  to  give  a 
pressure  of  1  pound  per  square  inch? 

15.  What  must  be  the  difference  in  height  between  a 
fire  hydrant  and  the  surface  of  the  water  in  a  city  res- 
ervoir to  give  a  pressure  of  50  pounds  per  square  inch 
at  the  hydrant  ? 

16.  In  figure  58,  the  U-tube  is  partly  filled  (BAC) 
with   mercury  whose  density   is   13.6   grams  per  cubic 
centimeter,  and  partly  (CD)  with  a  liquid  of  unknown 
density.     If  the  length  of  the  column  BA   is   5  centi- 
meters and  that  of  the  column   CD  is  75  centimeters, 
what  is  the  density  of  the  liquid  ? 


64.    Buoyant  effect  of  liquids.     When  swim- 
FJG.  58.— u-tube  ming  in  deep  water,  we  find  that  our  bodies  are 
and    'another  vejT  nearly  floated.     When  we  pick  up  a  stone 
liquid.  under  water,  we  find  it  much  heavier  if  we  lift 

it  above  the  surface.  Things  seem  to  be  lighter 
under  water ;  in  other  words,  water  buoys  up  anything  placed 
in  it.  In  order  to  find  how  much  lighter  anything  is  under 
water  than  it  is  out  of  water  let  us  try  the  following 
experiment. 

We  have  a  hollow  metal  cylindrical  cup  (7,  and  a  cylindrical  block 
B,  which  has  been  nicely  turned  to  fit  inside  the  cup  C.  We  hang  both 
from  a  beam  balance,  as  shown  in  figure  59,  and  counterbalance  with  a 
weight  W on  the  other  scalepan.  Then 
we  bring  a  glass  of  water  up  under 
the  block  B,  so  that  it  is  entirely 
under  water.  The  left-hand  side  of 
the  balances  rises,  which  shows  the 
upward  push  of  the  water  upon  B. 
But  we  can  restore  the  equilibrium 
again  by  pouring  water  into  the  cup 
C  until  it  is  just  filled.,  This  shows 
that  B  loses  in  apparent  weight  the 
weight  of  its  own  bulk  of  water.  If  we 
try  the  experiment,  using  kerosene 
instead  of  water,  we  find  that  exactly 
the  same  thing  is  true.  FIG,  59.  —  Buoyant  effect  of  liquids. 


MECHANICS   OF  LIQUIDS 


59 


65.  Archimedes'  principle.     The  principle  proved  by  this 
experiment  may  be  stated  as  follows :  — 

The  loss  of  weight  of  a  body  submerged  in  a  liquid  is  the 
weight  of  the  displaced  liquid. 

It  is  supposed  that  this  principle  about  the  loss  of  weight 
of  a  body  in  a  liquid  was  discovered  by  the  old  Greek  phi- 
losopher Archimedes  (287-212  B.C.).  Hiero,  king  of  Syra- 
cuse, suspected  a  goldsmith  who  had  made  a  crown  for  him, 
and  ordered  Archimedes  to  find  out  if  any  silver  had  been 
mixed  with  the  gold  in  the  crown.  To  do  this  without 
destroying  the  crown  seemed  a  puzzle  at  first,  but  one  day, 
while  Archimedes  was  in  the  public  bath,  he  noticed  that 
his  body  was  buoyed  up  by  the  water  in  which  it  was  sub- 
merged. Seeing  in  this  effect  the  solution  of  his  problem, 
he  leaped  from  the  bath  and  rushed  home  shouting,  "  Eureka  ! 
Eureka  ! "  (I  have  found  it !  I  have  found  it !). 

66.  Explanation  of  Archimedes'  principle.    This  principle  will 
be  readily  understood  from  the  following  example.     Suppose  we  place  a 
rectangular  block  in  ajar  of  water,  as  shown 

in  figure  60.  Let  the  block  be  10  x  6  x  4 
centimeters  and  let  the  top  be  5  centimeters 
below  the  surface  of  the  water,  and  the 
bottom  15  centimeters  beneath  the  surface. 
Then  the  pressure  on  top,  that  is,  the  down- 
ward push  on  each  square  centimeter,  is  5 
grams  and  the  pressure  on  the  bottom,  that 
is,  the  upward  push  on  each  square  centi- 
meter, is  15  grams.  Since  the  top  and 
bottom  each  have  an  area  of  6x4,  or  24 
square  centimeters,  the  whole  upward  push 
on  the  bottom  is  24  x  15,  or  360  grams, 
while  the  whole  downward  push  on  the  top 
is  only  24  x  5,  or  120  grams.  This  leaves 
a  net  upward  force  or  buoyancy  of  240 
grams.  But  this  is  exactly  the  weight  of 
the  displaced  water,  for  the  volume  of  the  displaced  water  is  10  x  6  x  4  = 
240  cubic  centimeters,. and  we  have  seen  in  section  11  that  this  much 
water  weighs  240  grains. 


FIG.    60. —  Lifting    effect    of 
water  on  submerged  block. 


60  PRACTICAL  PHYSICS 

The  same  sort  of  reasoning  would  hold  at  any  depth  and 
for  any  liquid  other  than  water  and  with  any  irregular- 
shaped  body.  So  it  may  be  said  that  in  any  liquid  of  any 
density  a  body  seems  lighter  by  the  weight  of  the  displaced 
volume  of  that  liquid. 

67.  Floating  bodies.     Let  us  think  what  will  happen  if 
this  upward  force,  or  buoyant  force,  is  more  than  the  weight 
of  the  body  submerged.     Evidently  the  body  will  rise  and 
will  continue  to  rise  as  long  as  the  upward  push  remains 
greater  than  the  downward  pull  of  gravity.     But  as  soon  as 
any  of  the  body  projects  above  the  surface,  less  water  is  dis- 
placed and  the  upward  push  is  less.     When  enough  of  the 
body  projects  to  reduce  the  buoyant  force  to  equality  with 
the  weight,  the  body  stops  rising  and  floats.     In  this  case  we 
see  that  the  loss  of  weight  is  the  whole  weight  itself. 

A  floating  body  displaces  its  own  weight  of  the  liquid  it  is 
floating  in. 

The  following  experiment  will  help  to  make  this  principle  of  Archi- 
medes, as  applied  to  floating  bodies,  seem  more  real.  Suppose  we  balance 

an  overflow  can  on  a  platform  scale, 
as  shown  in  figure  61.  The  can  is 
filled  with  water  so  that  it  just  over- 
flows and  is  balanced  by  the  weight 
on  the  other  platform.  We  will  place 
a  dish  to  catch  the  overflowing  water, 
and  then  put  a  block  of  wood  gently 
in  the  can.  After  the  water  has 
stopped  overflowing,  it  will  be  seen 
'"  «•»->£  balance.  This 
means  the  weight  of  water  which 
flowed  over  was  just  equal  to  the  weight  of  the  block.  This  can  be  veri- 
fied in  another  way  by  weighing  the  water  displaced  by  the  block. 

68.  Applications  of  Archimedes'   principle.     If   we   know 
the  total  weight  of  a  ship  and  its  equipment,  we  can  tell  at 
once  what  weight  of  water  it  will  displace,  and  so  it  is  possible 
to  compute  how  deep  it  must  sink  to  displace  its  own  weight 


MECHANICS   OF  LIQUIDS  61 

of  water.  It  is  also  evident  that  a  boat  must  sink  a  little 
deeper  in  fresh  water  than  in  salt  water,  and  will  sink  deeper 
when  loaded  than  when  empty.  A  submarine  boat  is  so 
constructed  that  it  is  only  slightly  lighter  than  water.  It 
can  then  be  submerged  by  letting  water  into  certain  tanks 
and  can  be  made  to  rise  by  pumping  the  water  out  of  the 
tanks.  This  same  idea  is  made  use  of  in  the  floating  dry- 
dock  shown  in  figure  62.  When  the  tanks  T,  T,  T  are  full 
of  water,  the  dock  sinks 
until  the  water  level  is  at 
LL.  The  ship  to  be  re- 
paired is  then  floated  into 
the  dock  and  the  water  is 
pumped  out  of  the  tanks  w- 
T,  T,  T.  As  the  com- 
partments are  emptied  of 

water,  the  dock  rises  until  the  water  level  is  at  the  line  TPJ  W, 
lifting  the  ship  out  of  water.  The  ship  and  dry-dock  still 
displace  their  own  weight  of  water,  but  the  displacement  is 
in  a  different  place. 

PROBLEMS 

1.  A  piece  of  stone  weighing  235  grams  in  air  and  128  grams  in  water 
is  put  into  a  dish  just  full  of  water.     How  much  water  runs  over? 

2.  A  rowboat  weighs  200  pounds.     How  many  cubic  feet  of  water 
does  it  displace  ? 

3.  A  barge  is  30  feet  long  and  16  feet  wideband  has  vertical  sides. 
When  a  large  elephant  is  driven  on  board,  it  sinks  4  inches  farther  in 
the  water.     How  many  tons  does  the  elephant  weigh  ? 

4.  What  is  the  volume  of  a  125-pound  boy,  if  he  can  float  entirely 
submerged  except  his  nose  ? 

5.  A  rectangular  block  is  22  centimeters  long,  6  centimeters  wide,  and 
4  centimeters  high,  and  floats  in  water  with  1  centimeter  of  its  height 
above  water.     How  much  does  it  weigh? 

6.  A  cube  5  centimeters  on  an  edge- weighs  600  grams  in  air.      How 
much  does  it  weigh  in  water  ? 

7.  How  much  will  a  cubic  foot  of  brass  (density  8.4  grams  per  cubic 
centimeter)  weigh  in  gasolene  (density  0.79  grams  per  cubic  centimeter)  ? 


62  PRACTICAL  PHYSICS 

'  8.  A  rectangular  solid  10  x  8  x  6  centimeters  is  submerged  in  water, 
so  that  the  top,  whose  dimensions  are  10  x  8  centimeters,  is  horizontal 
and  12  centimeters  below  the  water  surface. 

(a)  Find  the  total  force  pressing  down  on  the  top. 

(b)  Find  the  total  force  pushing  up  on  the  bottom. 

(c)  Find  the  loss  of  weight  of  the  solid. 

69.  Specific  gravity  and  density.     Archimedes'  principle 
furnishes  us  with   a  convenient   method  of  comparing   the 
weight  of  a  substance  with  the  weight  of  an  equal  bulk  of 
water.      The  ratio  of  these  weights  is   called   the   specific 
gravity  of  the  body.     In  other  words, 

weight  of  body 
Specific  gravity  =  — .  . .    .—     .  ,    „  J^ — 

weight  of  equal  bulk  of  water 

For  example,  a  piece  of  marble  weighs  100  grams  and  an  equal  bulk 
of  water  weighs  40  grams,  then  the  marble  is  100/40  or  2.5  times  as 
heavy  as  the  water.  The  specific  gravity  of  marble,  then,  is  2.5. 

The  term  specific  gravity  does  not  mean  quite  the  same 
thing  as  density.  The  specific  gravity  of  a  substance  is  an 
abstract  number  ;  for  example,  the  specific  gravity  of  mercury 
is  13.6.  But  the  density  of  a  substance  is  a  concrete  number  ; 
for  example,  the  density  of  mercury  is  13.6  grams  per  cubic 
centimeter,  or  850  pounds  per  cubic  foot. 

In  the  metric  system,  the  density  of  water  is  one  gram  per 
cubic  centimeter,  and  therefore 

Density  (g.  per  cm.3)  =.  (numerically)  specific  gravity. 

In  the  English  system,  the  density  of  water  is  62.4  pounds 
per  cubic  foot,  and  therefore 

Density  (Ibs.  per  cu.  ft.)  =  (numerically)  62.4  x  specific  gravity. 

70.  Methods  of  determining  specific  gravity  of  solids. 
GENERAL  RULE.     First  weigh   the   object.     Next  find  by 

some  indirect  method  the  weight  of  an  equal  bulk  of  water. 
Finally  divide  the  weight  of  the  object  by  the  weight  of  the 
equal  bulk  of  water. 


MECHANICS   OF  LIQUIDS 


63 


This  general  statement  covers  all  the  various  processes 
for  finding  the  specific  gravity  either  of  solids  or  of  liquids. 
The  different  procedures  vary  only  in  the  method  of  finding 
the  weight  of  an  equal  bulk  of  water. 

.  1st  Method.  If  the  object  is  a  regular  geometrical  solid,  you 
can  measure  its  dimensions  and  calculate  its  volume,  and  from 
that  get  the  weight  of  an  equal  bulk  of  water. 

2d  Method.  If  the  object  is  a  solid  that  will  sink  in  water, 
and  will  not  dissolve,  you  can  determine  its  loss  of  apparent 
weight  in  water.  This  is  the  weight  of  an  equal  bulk  of  water. 
That  is, 

weight  of  body 


Specific  gravity  = 


loss  of  weight  in  water 


For  example,  suppose  a  piece  of  copper  weighs  178  grams  in  air  and 
158  grams  in  water.  The  loss,  20  grams,  is  the  weight  of  an  equal  bulk 
of  water.  Therefore  the  specific  gravity  of  copper  =  178/20  =  8.9. 


3d  Method.  If  the  object  is  lighter  than 
water,  and  does  "not  dissolve,  select  a  suffi- 
ciently large  sinker  and  suspend  it  below  the 
object,  as  shown  in  figure  63.  Then  bring 
a  jar  of  water  up  under  the  whole  thing 
until  the  water  level  is  between  the  sinker 
and  the  object,  and  weigh.  Then  raise  the 
jar  still  farther  until  the  water  level  is 
above  the  object,  and  weigh  again.  This 
weight  will  be  less  than  the  first  because 
in  this  case  the  water  buoys  up  the  object, 
while  in  the  first  case  it  does  not.  The 
difference  between  the  two  weights  is  equal 
to  the  weight  of  the  water  displaced  by  the 
object. 


FIG.  63.  — Specific 
gravity  with 
sinker. 


Specific  eravit    - weight  of  body 

^  ~  lifting  effect  of  water  on  body  only* 


64  PRACTICAL  PHYSICS 

It  will  be  noticed  that  in  this  case  the  loss  of  weight  or 
lifting  effect  of  the  water  on  the  body  is  larger  than  the 
whole  weight.  This  is  why  the  body  floats. 

For  example,  suppose  a  piece  of  wood  weighs  120  grams  in  air,  and 
that,  with  a  suitable  sinker,  it  weighs  270  grams  when  the  sinker  is  under 
water,  and  90  grams  when  both  are  under  water.  Then  the  lifting  effect 
of  the  water  on  the  wood  is  270  —  90,  or  180  grams.  Therefore  the  spe- 
cific gravity  of  the  wood  is  120/180  =  0.667. 

71.    Specific  gravity  of  liquids. 

1st  Method.  Weigh  a  bottle  empty,  then  full  of  the  liquid, 
and  then  full  of  water.  Subtract  the  weight  of  the  empty 
bottle  in  each  case,  and  then  compare  the  weight  of  the  liquid 
with  the  weight  of  an  equal  volume  of  water. 

0      . .  weight  of  liquid 

Specie  gravity  =  weight  of  equal  volume  of  .water" 

Bottles,  called  specific  gravity  flasks  (Fig.  64),  are  made  for 
the  purpose  of  determining  the  specific  gravity  of  liquids 
with  great  accuracy  and  facility.  They  are 
usually  made  to  contain  a  definite  quantity  of 
pure  water  at  a  specified  temperature ;  for 
example,  250  grams. 

2d  Method.  Weigh  a  piece  of  glass  in  air, 
then  in  the  liquid,  and  then  in  water.  Find 
the  loss  of  weight  in  the  liquid  and  the  loss  of 
weight  in  water.  This  loss  of  weight  in  the 
liquid  is  the  weight  of  the  liquid  displaced, 
and  the  loss  of  weight  in  water  is  the  weight 

FIG.  64.— Specific  &  _, 

gravity  flask.       of  an  equal  volume  of  water.     Then 

loss  of  weight  in  liquid 

Specific  gravity  =  —  — 

loss  of  weight  in  water 

For  example,  suppose  the  glass  weighs  330  grams  in  air,  150  grams  in 
sulphuric  acid,  and  230  grams  in  water.  The  glass  loses  180  grams  in 
acid  and  100  grams  in  water.  Since  these  are  the  weights  of  equal  volumes 
of  acid  and  water,  the  specific  gravity  of  the  acid  —  180/100  =  1.8. 


MECHANICS   OF  LIQUIDS  65 

3d  Method.  *  The  most  common  way  of  determining  the  spe- 
cific gravity  of  liquids  is  by  the  hydrometer.  This  is  usually 
made  of  glass,  and  consists  of  a  cylindrical  stem  and  a  bulb 
weighted  with  mercury  or  shot  to  make  it  float  upright 
(Fig.  65).  The  liquid  is  poured  into  a  tall  jar,  and  the  hy- 
drometer is  gently  lowered  into  the  liquid  until  it  floats  freely. 
The  point  where  the  surface  of  the  liquid 
touches  the  stem  of  the  hydrometer  is  noted. 
There  is  usually  a  paper  scale  inclosed  inside 
the  stem,  so  made  that  the  specific  gravity  (or 
density  in  grams  per  cubic  centimeter)  can  be 
read  off  directly.  In  light  liquids,  like  kero- 
sene, gasolene,  and  alcohol,  the  hydrometer 
must  sink  deeper  to  displace  its  weight  of 
liquid  than  in  heavy  liquids  like  brine,  milk, 
and  acids.  In  fact  it  is  usual  to  have  two 
separate  instruments,  one  for  heavy  liquids, 
on  which  the  mark  1.000  for  water  is  near 
the  top,  and  one  for  light  liquids,  on  which 
the  mark  1.000  is  near  the  bottom  of  the  FIG.  65. 

Stem.  Hydrometer. 

72.  Commercial  uses  of  the  hydrometer.  Since  the  com- 
mercial value  of  many  liquids,  such  as  sugar  solutions,  sul- 
phuric acid,  alcohol,  and  the  like,  depends  directly  on  the 
specific  gravity,  there  is  extensive  use  for  hydrometers. 
Perhaps  the  best-known  form  of  hydrometer  is  the  kind  used 
in  testing  milk,  called  a  lactometer.  The  specific  gravity  of 
cow's  milk  varies  from  1.027  to  1.035.  Since  only  the  last 
two  figures  are  important,  the  scale  of  a  lactometer  is  made 
to  run  from  20  to  40,  which  means  from  1.020  to  1.040. 
The  specific  gravity  of  milk  does  not  give  us  a  conclusive 
test  as  to  its  worth.  Milk  contains  besides  the  water 

*  There  is  another  method,  using  balancing  columns,  which  will  be  de- 
scribed in  the  Laboratory  Manual.  To  understand  it  one  must  have  read 
Chapter  IV. 

F 


66  PRACTICAL  PHYSICS 

(which  is  about  87  %)  some  substances  which  are  heavier 
than  water,  such  as  albumen,  sugar,  and  salt,  and  others  that 
are  lighter  than  water,  such  as  butter  fat.  Besides  the 
specific  gravity,  one  needs  to  determine  the  amount  of  fat, 
and,  if  possible,  the  other  solids  in  the  milk,  in  order  to 
know  its  richness.  Of  course  the  very  important  question  as 
to  the  cleanliness  of  milk  must  be  left  to  the  bacteriologist. 

PROBLEMS 

1.  A  piece  of  ore  weighs  42  grams  in  air  and  25  grams  in  water. 
Calculate  its  specific  gravity. 

2.  A  stone  weighs  15  pounds  in  air  and  9  pounds  in  water. 

(a)  Find  its  specific  gravity. 

(b)  Find  its  density  in  the  metric  system. 

(c)  Find  its  density  in  the  English  system. 

3.  A  body  has  a  specific  gravity  of  3.5.     What  is  its  density  in  (a)  the 
metric  system,  and  (b)  the  English  system? 

4.  If  the  specific  gravity  of  lead  is  11.4,  how  many  cubic  centimeters 
of  lead  does  it  take  tojnake  a  kilogram  weight? 

5.  If  the  specific  gravity  of  cork  is  0.25,  how  many  cubic  feet  of  cork 
are  there  in  1  pound  of  cork  ? 

6.  A  block  of  wood,  15  x  10  x  8  centimeters,  floats  with  one  of  its 
largest  sides  2  centimeters  out  of  water. 

(a)  Find  its  weight. 

(b)  Find  its  specific  gravity. 

7.  A  plank  8  centimeters  thick  floats  with  5  centimeters  under  water. 
Find  its  specific  gravity. 

8.  A  block  of  wood  weighs  150  grams ;  a  sinker  is  suspended  from  it, 
and  when  the  sinker  is  under  water  and  the  block  is  in  air,  the  combina- 
tion weighs  350  grams.     When  the  wood  and  the  sinker  are  both  under 
water,  they  weigh  100  grams.     Find  (a)  the  volume  of  the  block  of  wood, 
and  (£)  its  specific  gravity. 

9.  A  cube  of  iron   10  centimeters  on  an  edge  (specific  gravity  7.5) 
floats  in  mercury  (specific  gravity  13.6).     How  many  cubic  centimeters 
are  above  the  mercury? 

10.  A  can  weighs  190  grams  when  empty,  600  grams  when  full  of 
water,  and  613  grams  when  full  of  milk. 

(a)   What  is  the  capacity  of  the  can  in  cubic  centimeters? 
(6)  What  is  the  specific  gravity  of  the  milk  ? 

11.  How  much  does  1  cubic  centimeter  of  lead  (specific  gravity  11.4) 
weigh  in  kerosene  (specific  gravitv  0.79)  ? 


MECHANICS   OF  LIQUIDS  67 

12.  A  bottle  weighs  80  grams  empty,  280  grains  when  filled  with 
water,  and  250  grains  when  filled  with  a  medicine.     What  is  the  specific 
gravity  of  the  medicine? 

13.  An  empty  bottle  weighs  50  grams ;  the  same  bottle  full  of  water 
weighs  200  grams.     Some  sand  is  put  into  the  empty  bottle  and  it  then 
weighs  320  grams.     Finally  the  bottle  is  filled  with  water,  and  the  bottle, 
sand,  and  water  weigh  370  grams. 

(a)  Find  the  capacity  of  the  bottle. 

(6)  Find  the  volume  of  the  sand. 

(c)  Find  the  specific  gravity  of  the  sand. 

14.  If  one  buys  10  pounds  of   mercury  (specific  gravity  13.6),  how 
many  cubic  inches  should  one  get? 

15.  If  the  inside  of  an  ice  chest  measures  24  x  18  x  12  inches,  how 
many  pounds  of  ice  (specific  gravity  0.92)  will  it  hold  ? 

16.  How  many  pounds  of  sulphuric  acid  (specific  gravity  1.84)  does 
a  5-gallon  carboy  contain  ? 

73.  City  waterworks.     Every  city  has  to  face  the  problem 
of  providing  a  plentiful  supply  of  pure  water  for  household 
use,  for  industrial  purposes,  and  for  fire  protection.     Not 
only  must  there  be  enough  water,  but  it  must  be  furnished 
at  sufficient  pressure  to  force  it  to  the  tops  of  high  buildings. 
If  the  city  is  located  near  the  mountains,  as  are  Denver  and 
Los  Angeles,  it  is  an  easy  matter  to  conduct  the  water  from 
an  elevated  reservoir  in  large  pipes  or  mains  to  the  houses. 
Since  the  water  tends  to  seek  its  own  level,  it  will  rise  in  the 
buildings  to  the  height  of  the  reservoir.     But  in  most  cities, 
such   as   New  York,  Philadelphia,  and  Boston,  the  gravity 
system  of  waterworks  is  impossible  and  a  pumping  system 
must  be  employed.     The  operation  of  the  big  steam  pumps 
that  are  used  will  be  explained  later  (section  100). 

74.  Hydrants  and  faucets.     The  only  parts  of  this  great 
system  of  water  pipes  which  we  ordinarily  see  are  the  hydrants 
on  the  edge  of  our  sidewalks,  and  the  taps  or  faucets  at  our 
sinks  and  bathtubs.      These  are  merely  valves  for  opening 
and  closing  the  pipes,     The  internal  construction  of  the  or- 
dinary tap  is  shown  in  figure  66.      The  handle  operates  a 
screw  which  forces  a  disk,  faced  with  a  fiber  washer,  against 


68 


PRACTICAL  PHYSICS 


a  circular  opening  or  seat,  and  so  shuts 
off  the  water.     If  the  handle  is  turned 
the  other  way,  the  disk   is  raised,  leav- 
ing an  opening.     This  sort  of  valve  may 
get  out  of  order  in  two  ways  :    the  fiber 
washer   may  wear  out  and  the  packing 
about    the   handle    rod    may   get    loose. 
FIG.  66.— Cross  section    Both   of   these    can   be    easily   replaced, 
of  common  faucet.       The    packing    consists   of   cotton   twine 
wrapped  around  the  valve  stem,  and  is   held   in   place  by 
what  is  called  a  gland. 

75.  How  we  measure  water  pressure.  Doubt- 
less we  have  all  found  that  water  flows  slowly 
from  a  faucet  on  an  upper  floor.  This  is  because 
the  water  pressure  is  low  there.  To  measure 
it,  we  use  some  form  of  pressure  gauge,  and  for 
as  small  a  pressure  as  this  would  be,  an  open 
mercury  manometer  would  be  the  most  accurate 
form  of  pressure  gauge.  It  consists  of  a 
U-shaped  tube  filled  with  mercury,  as  shown 
in  figure  67. 

Suppose  the   water  pressure  is  enough  to  balance  a    FIG.    67.  —  Mer- 
mercury  column  4  feet  high.    How  much  is  the  pressure       cury   pressure 
in  pounds  per  square  inch?     A  column  of  mercury  4       gauge, 
ieet  high  and  1  square  inch  at  the  base  would  contain 
48  cubic  inches,  and  \vould  weigh  23.5   pounds.     Therefore  the  pres- 
sure of  the  water  would  be  23.5  pounds  per  square  inch.     With  such 
a  gauge  it  is  easy  to  show  that  the  water  pressure  is  less  on  the  top  floor 
than  in  the  basement. 

A  mercury  gauge  is  so  cumbersome  and  expensive  that  a 
Bourdon  spring  gauge  is  generally  used.  It  consists  of  a 
brass  tube  of  elliptical  section,  bent  into  a  nearly  complete 
ring,  and  closed  at  one  end,  as  shown  in  figure  68.  The 
flatter  sides  of  the  tube  form  the  inner  and  outer  sides  of  the 
ring.  The  open  end  of  the  tube  is  connected  with  the  pipe 


MECHANICS   OF  LIQUIDS 


69 


through  which  the  liquid  under  pressure  is  admitted.  The 
closed  end  of  the  tube  is  free  to  move.  As  the  pressure  in- 
creases the  tube 
tends  to  straighten 
out,  moving  a 
pointer  to  which 
it  is  connected  by 
levers  and  small 
chains.  These 
spring  gauges 
have  the  scale  so 

graduated     that  FIG.  68.  —  Bourdon  gauge. 

they  read  directly  in  pounds  per  square  inch. 

76.  Fluctuations  in  water  pressure.  Not  only  does  one  find 
a  decrease  of  water  pressure  in  going  from  the  basement  to  the 
attic  of  a  house,  but  if  the  gauge  is  attached  at  one  point  and 
watched  closely,  it  will  be  seen  to  fluctuate  according  as  much 
or  little  water  is  being  drawn  elsewhere  in  the  building. 

The  following  experiment  shows  the  same  thing  on  a  smaller  scale. 
The  tank  or  reservoir  R  in  figure  69  is  connected  with  a  supply  pipe  AB. 

The  pressure  along  the  pipe 
is  indicated  by  the  height 
of  the  water  in  the  tubes 
C,  A  and  E.  When  the 
pipe  is  closed  at  B,  the  level 
is  the  same  in  R,  C,  Z>,  and 
E ;  this  is  called  the  static 
condition.  But  when  the 
jp^ga^  stopper  is  removed  from  B, 
g  N^\\  and  water  flows  out,  the 

FIG.  69.  -Pressure  falls  with  flow.  "*  P»»sure    is   no  longer  the 

same  at   all   points    along 

the  pipe,  but  falls  off  as  the  distance  from  the  reservoir  R  increases. 
Tli  is  drop  in  pressure  is  due  to  friction  against  the  walls  of  the  pipe 
through  which  the  water  has  to  run. 

From  this  experiment*  we  see  that,  when  a  number  of 
faucets  are  open  and  the  water  is  flowing,  the  pressure  in  the 


70 


PRACTICAL  PHYSICS 


neighborhood  becomes  small.  *Bo.  equalize  these  changes  in 
water  pressure  and  also  to  pro\£de  fsome  flexibility  in  the 
system,  it  is  quite  common  to  havefci  fltandpipe  in  the  water 
system  nearer  the  houses  than  the  main  reservoir.  This  also 
serves  as  an  auxiliary  reservoir  in  case  of  emergency. 

77.  Water  meter.  It  is  common  now  to  measure  the 
quantity  of  water  which  is  used  by  each 
house.  This  is  done  by  an  instrument 
called  a  water  meter.  There  are  several 
types  of  these  meters;  one  of  the  sim- 
plest is  shown  in  figure  70,  and  its  action 
is  shown  in  the  four  diagrams  in  figure 
71.  The  water  enters  through  the  left- 
hand  kidney-shaped  opening,  shown  by 
dotted  lines,  and  leaves  through  the  simi- 
lar opening  at  the  right.  The  moving 
part,  shown  by  the  heavy  line,  has  a  hub 
(tlie  black  circle)  that  travels  around  in 
the  little  circular  track  provided  for  it,  the  moving  part 
meanwhile  oscillating  to  and  fro  without  turning  completely 
around.  This  makes  the  various  annular  spaces  enlarge 
as  long  as  they  are  in  connection  with  the  inlet  (watch, 


FIG.  70.  —  Water  meter. 


FIG.  71. —  Diagrams  to  show  operation  of  water  meter. 

for  example,  the  space  marked  a  in  the  diagrams)  and  con- 
tract when  they  are  in  connection  with  the  outlet  (watch, 
for  example,  the  space  marked  5).  In  this  way  each  space 
measures  out  its  appropriate  quantity  of  water  and  delivers 
it  to  the  outlet  pipe.  The  number  of  revolutions  of  the  hub 


MECHANICS   OF  LIQUIDS 


71 


FIG.  72.  —  Meter  dials. 


is  registered  on  a  series  of  dials  (see 
figure  72)  which  indicate  the  number 
Df  cubic  feet  that  have  passed  through 
the  meter.  Thus  the  dials  in  figure 
72  indicate  94,450  cubic  feet.  The 
official  of  the  water  department  reads 
these  dials  periodically,  and  by  sub- 
tracting can  easily  compute  the  water 
consumed  during  the  period,  and  so 
fix  the  charge  in  proportion. 

78.  Water   motors.      In   cities   where    water   is  supplied 
under  considerable  pressure,  it  may  be  used  to  run  sewing 

machines,  small  polishers,  grinders,  lathes, 
etc.,  by  means  of  a  water  motor.  A  simple 
form  is  shown  in  figure  73.  The  stream  of 
water  is  made  to  pass  through  a  small  open- 
ing at  high  velocity  and  to  strike  against 
some  blades  or  buckets  on  the  rim  of  a  wheel. 
The  wheel  is  inclosed  in  a  metal  case,  from 
which  the  water  flows  away  to  the  drain- 
pipe. The  impact  of  the  water  against  the 
blades  turns  the  shaft,  to  which  the  machines 
to  be  driven  are  connected  either  directly  or 
by  belts. 

79.  Water  wheels.     Just  as  a  small  stream  of  water  may 
be  used  to  turn  small  machinery,  so  it  is  possible  to  make 
large  streams  of  water  turn  large  machines,  which  saw  wood, 
grind  corn,  and  furnish  electric  lights  for  streets  and  houses. 
Any  community  possessing  a  waterfall  or  a  rapid  in  a  river 
has  a  valuable  source  of  power.     The  older  types  of  water 
wheels   were    the  overshot,  where   the  weight   of   the   water 
slowly  turns  the  wheel,  and  the  undershot,  where  the  wheel  is 
let  down  into  a  swiftly  flowing  current.     The  modern  forms 
of  water  wheels  are  the  Pelton  wheel  and  the  turbine.     The 
little  water  motor  described  above  is  a  typical  form  of  Pelton 


FIG.  73.  —  Water 
motor. 


72 


PRACTICAL  PHYSICS 


wheel,  the  parts  of  a  commercial  wheel 
being  the  same,  but  much  larger  (see 
plate  facing  page  72).  The  efficiency 
of  this  type  of  wheel  is  much  greater 
than  that  of  the  undershot  wheel,  and 
sometimes  runs  as  high  as  83  %.  By  far 
the  most  important  type  of  water  wheel 
to-day  is  the  turbine.  This  is  somewhat 
like  a  windmill.  The  water  is  conducted 
from  the  reservoir  above  the  dam  through 
a  cylindrical  tube  to  a  "  penstock"  which 
surrounds  the  case  of  the  wheel  (Fig. 
74).  This  case  stands  on  the  floor  of  the 
penstock  and  is  submerged  in  water  to  a 
depth  equal  to  the  "  head  "  or  height  of 
water  supply.  The  water  is  not  let  into 
the  case  about  the  wheel  at  one  opening, 
but.  through  many  inlets  or  passages, 
which  are  so  curved  as  to  direct  the 


Stationary 


water  against  the  blades  of  the 
wheel  in  the  most  favorable  direc- 
tion to  produce  rotation,  as  shown 
in  figure  75.  The  wheel  is  attached 
to  a  shaft  which  transmits  the  power 
to  the  machinery  above.  A  small 
shaft  controls  the  size  of  the  inlet 
openings  in  the  case.  When  the 
water  has  done  its  work,  it  falls 
from  the  bottom  of  the  wheel  case 
into  the  "tail  race"  below  the 
penstock.  These  turbines  some- 
times have  an  efficiency  of  90  %. 

Pelton  wheels  are  used  in  general  where  the  fall  is  high 
and  the  quantity  of  water  small,  turbines  where  the  fall  is 
low  and  the  quantity  of  water  great. 


Stationary 

FIG.  75.  —  Stationary  and  moving 
blades  of  water  turbine. 


Pelton  water  wheel,  to  be  installed  at  Rjnkan,  in  Norway,  where  it  will  develop 
7500  horse  power.    The  wheels  of  small  water  motors  are  similar  in  shape. 


MECHANICS   OF  LIQUIDS  73 

PROBLEMS 

1.  The  water  level  in  a  tank  on  top  of  a  building  is  100  feet  above 
the  ground.     What  is  the  pressure  in  pounds  per  square  inch  at  a  faucet 
10  feet  above  the  ground  ? 

2.  If  200  cubic  feet  of  water  flow  each  second  over  a  dam  25  feet 
high,  what  is  the  available  power? 

3.  If  the  efficiency  of  the  water  wheel  used  at  the  dam  described  in 
problem  2  is  65  %,  how  many  horse  power  can  it  supply  ? 

4.  How  many  cubic  feet  of  water  must  be  supplied  every  second  to  an 
overshot  wheel  which  is  20  feet  in  diameter  and  delivers  40  horse  power 
at  an  efficiency  of  85%? 

5.  The  Niagara  turbine   pits    are   136  feet   deep,   and   the   average 
horse  power  of  the  turbines  is  5000.     Their  efficiency  is  85%.     How 
many  cubic  feet  of  water  does  each  turbine  handle  per  minute  ? 

80.  Molecular  attractions.       When  a  drop  of  water  falls 
through  the  air,  it  draws  itself  into  an  almost  perfect  sphere. 
Similarly,  lead  shot  are    made    by  letting  molten  lead  fall 
from  a  sieve  at  the  top  of  a  tower  into  a  pool  of  water  at 
the  bottom.     In  general,  a  liquid  when  left  to  itself  tends  to 
get  into  the  shape  which  has  the  smallest  possible  surface, 
as  if  it  were  composed  of  little   particles  which  had  great 
attraction  for  one  another.     It  is  also  observed  that  there  is 
a  great  attraction  between  many  pairs  of  substances  if  they 
are  brought  very  close  together,  as  between  wood  and  glue, 
stone  and  cement,  paint  and  wood.     When  this  attraction  is 
between  particles  of  the  same  kind,  it  is  called  cohesion,  and 
when  between  particles  of  different  kinds,  it  is  called  adhesion. 

In  soap  bubbles,  it  is  the  cohesion  of  the  little  particles  of 
soapsuds  which  makes  the  thin  film  act  like  an  elastic  mem- 
brane. It  is  this  same  property  of  liquids  which  makes  it 
possible  to  lay  a  somewhat  greasy  needle  on  the  surface  of 
water  and  have  it  float,  although  steel  is  eight  times  as  dense 
as  water. 

81.  Capillarity.     Suppose  we   have  two  U- tubes    (Fig.   76)   with 
their  side  tubes  30  mm.  and  1  mm.  in  diameter.    If  we  pour  water  colored 
with  ink  into  the  first  tube,  and  mercury  into  the  second  tube,  we  observe 


74 


PRACTICAL   PHYSICS 


that  in  each  case  the  surfaces  in  the  two  sides 
of  the  U-tube  are  not  at  the  same  level. 

The  water  wets  the  surface  of  the 
glass  and  is  attracted  by  it,  i.e.  the 
adhesion  is  great.  The  mercury  does 
not  wet  the  glass,  and  the  cohesion  of 
particles  of  mercury  for  each  other 
makes  it  appear  as  if  there  were  repul- 
sion between  glass  and  mercury.  The 
FIG.  76.  -  Capillarity  in  surface  of  the  merCury  is  convex,  and 

small  tubes.  J 

it  stands  at  a  lower  level  in  the  nar- 
row tube  than  in  the  wide  one.  In  the  case  of  water,  each 
tube  is  drawing  the  liquid  up  into  itself  against  the  pull  of 
gravity.  The  narrower  the  tube,  the  higher  the  liquid  is 
raised.  Since  these  small  tubes  have  haiiiike  dimensions, 
they  are  called  capillary  tubes  (from  Latin  capillus,  a  hair), 
and  this  phenomenon  is  called  capillarity.  In  this  way  liquids 
rise  in  wicks,  in  filter  paper,  and  in  the  soil. 

SUMMARY   OF   PRINCIPLES   IN    CHAPTER   III 

force 


Pressure  = 


area 


Force  =  pressure  x  area. 


For  liquids  under  pressure  (weight  of  liquid  negligible  in  com- 
parison) :  — 

Pressure  everywhere  the  same. 
Force  varies  as  area. 

For  liquids  with  a  free  surface  (weight  of  liquid  the  only  thing  that 
counts) :  — 

Pressure  proportional  to  depth,  independent  of  direction, 

Proportional  to  density  of  liquid, 

Equal  to  weight  of  a  column  of  liquid  with  a  base  one  unit 

square  and  a  height  equal  to  the  depth. 

Average  pressure  on  a  surface  =  pressure  at  center  of  surface. 
Total  force  on  a  surface  =  average  pressure  x  area. 


MECHANICS   OF  LIQUIDS  75 

Archimedes'  principle :  — 

The  loss  of  weight  of  a  body  either  partly  or  wholly  submerged 

in  a  liquid  is  equal  to  the  weight  of  the  displaced  liquid. 
If  the  body  just  floats,  this  loss  of  weight  is  also  equal  to  the 

weight  of  the  body. 

Density  =  weight  of  body  ^ 
volume  of  body 

Specific  gravity  =  -  weight  of  body 

weight  of  equal  volume  of  water 

In  the  metric  system,  since  1  cu.  cm    of  water  weighs    1  gram, 

Density  (g.  per  cm.3)  =  (numerically)  specific  gravity. 
In  the  English  system,  since  1  cu.  ft.  of  water  weighs  62.4  Ibs., 
Density  (Ib.  per  ft.3)  =  (numerically)  62.4  x  specific  gravity. 

To  get  specific  gravity :  — 

Find  weight  of  body. 

Find  weight  of  equal  volume  of  water. 

Divide. 

To  get  weight  of  equal  volume  of  water :  — 

1.  Compute  volume.     Weight  of  water  =  volume  x  density  of 

water. 

2.  Loss  of  weight  of  body  when  wholly  submerged  —  weight  of 

equal  volume  of  water.     (May  have  to  use  sinker.) 

3.  Weigh  equal  volumes  of  liquid  and  of  water  in  a  bottle. 

4.  Find  loss  of  weight  of  a  solid  in  the  liquid  and  in  water. 

(May  use  either  sinker  or  float,  i.e.  hydrometer.) 

5.  Use  balancing  columns  (see  laboratory  manual). 

QUESTIONS 

1.  What  advantages  has  the  hydraulic  press  in  testing  steam  boilers? 

2.  What  device  is  used  to  prevent  the  oil  or  water  from  leaking  out 
around  the  pistons  of  a  hydraulic  press  ? 

3.  How  is  Archimedes  supposed  to  have  done  his  famous  experiment 
with  the  crown? 


76  PRACTICAL  PHYSICS 

4.  When  a  ship  passes  from  a  river,  where  the  water  is  fresh,  into  the 
ocean,  does  it  rise  or  sink  in  the  water? 

5.  If  you  have  a  table  of  densities  in  the  metric  system,  how  could 
you  make  a  table  of  specific  gravities? 

6.  How  could  you  determine  the  specific  gravity  of  a  solid  soluble  in 
water,  but  insoluble  in  kerosene  ? 

7.  What  is  the  water  pressure  in  your  laboratory? 

8.  Why  has  skimmed  milk  a  greater  density  than  normal  milk? 

9.  Two  faucets  in  a  town  show  the  same  pressure  on  the  gauge  and 
are  the  same  size.     If  one  is  one  mile  from  the  reservoir,  and  the  other 
is  two  miles  away,  will  each  faucet  deliver  the  same  quantity  of  water 
per  minute  when  opened  wide  ? 

10.  Sometimes  when  a  faucet  is  opened,  especially  on  an  upper  floor, 
the  water  comes  with  a  rush  at  first  and  much  more  slowly  after  it  has 
been  running  a  few  seconds.     Explain. 

11.  Why  does  one  need  to  take  temperature  into  account  in  using  the 
lactometer? 

12.  What  metals  float  in  mercury? 

13.  How  can  one  pour  a  liquid  out  of  a  glass  with  the  aid  of  a  spoon 
or  glass  rod,  so  that  it  will  not  run  down  the  side  of  the  glass  ? 

14.  Explain  the  action  of  a  towel ;  of  a  sponge. 

15.  Explain  the  process  of  "  fire-polishing  "  the  broken  end  of  a  glass 
tube. 

16.  If  you  know  the  displacement  of  a  battleship,  how  could  you  find 
its  weight? 

17.  Why  does  one  use  snowshoes  in  walking  over  deep  snow? 

18.  Why  is  it  easier  to  float  when  swimming  in  the  ocean  than  in  a 
river  ? 

19.  Why  should  life  preservers  be  filled  with  cork  instead  of  hay? 

20.  A  schoolboy  in  Holland  is  said  to  have  saved  his  country  from  a 
flood  by  thrusting  his  arm  into  a  hole  in  the  dike  150  centimeters  below 
the  surface  of  the  sea.     Could  a  small  boy  hold  back  the  whole  North 
Sea? 


CHAPTER  IV 
MECHANICS    OF    GASES 

Liquids  and  gases  differ  in  compressibility  —  air  compressors 
—  uses  —  Boyle's  law — vacuum  pumps  —  uses  —  weight  of  the 
air  —  atmospheric  pressure  —  measured  by  Torricelli's  experi- 
ment—  barometer  and  its  uses  —  pressure  gauges  —  lifting  effect 
of  air  —  uses  in  balloons  and  pumps  for  liquids —  other  proper- 
ties of  gases  —  absorption  and  diffusion  —  molecular  theory. 

COMPRESSED  AIR 

82.  Pneumatic   machines.     Just   as    hydraulic    machines 
make  use  of  the  properties  of  liquids,  so  pneumatic  machines 
make  use  of  the  properties  of  gases.     Nowadays  we  often  clean 
our  houses  with  vacuum  pumps  ;  we  stop  our  express  trains 
with  air  brakes ;  we   drive  the   drills  and  hammers  in  our 
shops  with  compressed  air;  and    we   have  begun  to  travel 
through  the  air  with  dirigible  balloons  and  flying  machines. 
To  understand  the  operations  of  all  these  machines,  we  must 
study  the  properties  of  gases. 

83.  Liquids  and  gases  alike  in  some  respects.     Liquids  and 
gases  are  called  fluids,  because  they  have  no  definite  shape, 
but  adapt  themselves  to  the  shape  of  the  vessel  containing 
them.     A  liquid,  however,  has  a  definite  volume  under  ordi- 
nary conditions,  filling  the  lower  part  of  a  containing  vessel, 
and  being  bounded  by  a  free  surface  above.     A  gas,  on  the 
other  hand,  has  no  fixed  volume  and  no  free  surface,  but  fills 
the  whole  of  its  containing  vessel  at  once  if  the  vessel  is 
closed,  and  escapes  if  the  vessel  is  open  at  the  top.     So  the 
little  particles  of  a  gas  have  much  more  mobility  than  those 
of  a  liquid. 

77 


78 


PRACTICAL  ^HYSICS 


Gases  and  liquids  are  alike  in  that  each,  when  under  pres 
sure,  distributes  that  pressure  undiminished  in  all  directions 
in  accordance  with  the  principle  of  Pascal. 

The  gauges  which  are  used  to  measure  gas  pressure  are 
often  the  same  gauges  that  would  be  used  to  measure  the 
pressure  exerted  by  a  liquid  (see  section  75). 

84.    Air  is   very  compressible.     In  one  respect  gases  are 
very  different  from  liquids,  namely,  in  compressibility.     This 
striking  difference  can  be  shown    in    the  fol- 
lowing experiment. 

When  a  brass  tube,  with  a  closely  fitting  steel  rod 
(Fig.  77),  is  filled  with  air,  the  steel  plunger  can  be 
easily  pushed  down  by  hand,  and  when  the  plunger  is 
released,  it  springs  back  nearly  to  its  initial  position.  If 
it  does  not  come  quite  back  to  its  initial  position,  it 
means  that  some  of  the  air  has  leaked  out.  The  en- 
trapped air  acts  like  a  spring.  But  when  .the  tube  is 
filled  with  water,  or  any  other  liquid,  it  is  quite  impos- 
sible to  push  the  plunger  down,  to  any  perceptible  ex- 
tent, by  hand,  and  when  the  end  of  the  plunger  is  struck 
with  a  hammer,  the  effect  is  as  if  the  entire  tube  were  a 
solid  steel  column,  because  the  liquid  is  so  nearly  incom- 
pressible. 


FIG.  77.— Com- 
pressibility of 
fluids. 


85.  Air  compressors.  The  simplest  form  of  air  com- 
pressor is  the  ordinary  bicycle  pump,  such  as  is  used  to  in- 
nate the  tires  on  bicycles  and  automobiles.  Figure  78  shows 
a  sectional  view  of  such  a 
pump  attached  to  a  tire.  It 
consists  of  a  cylinder  O  and 
piston  P.  On  the  down 
stroke  some  air  is  entrapped 
below  the  piston  and  com- 
pressed, its  pressure  rising 
until  it  becomes  equal  to  that 
of  the  air  already  in  the  tire. 
Then  the  valve  S  opens,  and  FIG.  78.— Air  compressor. 


MECHANICS   OF  GASES 


79 


during  the  rest  of  the  down  stroke  the  air  is  forced  into  the 
tire.  When  the  up  stroke  starts,  this  valve  closes  and 
the  leather  washer  on  the  piston  bends  down  and  allows  air 
to  flow  past  the  piston  into  the  cylinder  below.  Then  on 
the  next  down  stroke  this  air,  entrapped  by  the  spreading 
of  the  leather  flange,  is  compressed  and  forced  over  into  the 
tire.  There  is  only  one  valve,  and  that  is  in  the  stem  of 
the  tire. 

Large  air  compressors  driven  by  steam  engines  or  electric 
motors  are  much  used  in  steel  plants,  shops,  and  quarries  to 
furnish  a  supply  of  compressed  air.  This  is  delivered  as  a 
forced  draft  to  blast  furnaces,  or  stored  in  steel  tanks  and 
used  to  drive  all  sorts  of  pneumatic  machinery. 

86.  Uses  of  compressed  air.  There  are  many  tools  which 
are  driven  by  compressed  air,  such  as  riveting  hammers  for 
forming  the  riveted  heads  on  steel  work,  and  the  pneumatic 
tools  used  in  stone  cutting,  iron  chipping,  drilling,  etc.  These 
are  in  general  lighter  and  simpler 
than  other  portable  tools,  and  there 
is  less  danger  of  fire.  When  such 
tools  are  used  in  mines,  the  waste 
air  which  they  discharge  helps  to 
furnish  ventilation,  and  this  is 
often  an  important  advantage. 
Rock  drills,  and  sand  blasts  for  clean- 
ing metal  and  stone  surfaces,  are 
other  common  applications.  But 
perhaps  the  most  interesting  ap- 
plication is  the  air  brake. 

The  essential  parts  of  the  Westing- 
house  air  brake  are  shown  in  figure  79. 
P  is  the  train  pipe  leading  from  a  large 
reservoir  on  the  engine,  in  which  the  air 

is  maintained  at  a  pressure  of  about  75         pIG<  79  _  Westinghouse  air 
pounds  per  square  inch.     As  long  as  this  brake. 


80  PRACTICAL  PHYSICS 

pressure  is  applied  to  the  automatic  valve  V  there  is  maintained  a  com 
munication  between  P  and  an  auxiliary  tank  R  under  each  car,  and  at 
the  same  time  air  is  cut  off  from  the  brake  cylinder  C.  But  whenever 
the  pressure  in  P  drops,  either  by  the  moving  of  a  lever  in  the  engine 
cab  or  by  the  accidental  parting  of  a  hose  coupling,  the  valve  V  shuts  off 
P  and  connects  the  reservoir  R  with  the  cylinder  C.  This  pressure  on 
the  piston  in  C  forces  the  brakes  against  the  wheels.  As  soon  as  the 
pressure  in  the  pipe  is  restored,  the  valve  V  reestablishes  the  connection 
between  P  and  R,  and  at  the  same  time  the  air  in  C  escapes.  The 
spring  S  then  releases  the  brakes  by  pushing  up  the  piston. 

87.  How  volume  of  air  changes  with  pressure  —  Boyle's 
law.  In  studying  about  compressed  air  we  are  soon  con- 
fronted with  the  question  as  to  how  much  the  volume  of  a 
given  quantity  of  air  changes  as  the  pressure  changes.  This 
was  first  investigated  for  the  case  where  the  temperature  of 
the  air  does  not  change  during  compression,  by  an  Irishman, 

Robert  Boyle  (1626-1691),  and  a 
few  years  later  by  a  Frenchman, 
Mariotte.  The  results  of  their  ex- 
periments showed  that  if  we  start 


FIG.  80.  —  Compression  of      with     a    given   volume    of    air    V, 
subjected  to  a    certain   pressure  P 

(Fig.  80),  and  double  the  pressure,  the  volume  of  air  will 
be  reduced  to  one  half.  If  the  pressure  be  made  three  times 
as  great,  the  volume  of  the  air  will  be  reduced  to  one  third, 
provided  the  temperature  of  the  air  is  kept  constant.  This 
principle  is  known  as  Boyle's  law  and  applies  to  all  gases. 
It  may  be  stated  as  follows  :  The  volume  of  a  gas  at  constant 
temperature  varies  inversely  as  the  pressure. 
This  may  also  be  expressed  in  symbols  as 

P  :  P1  :  :  V  :  V (notice  the  inverse  proportion), 
or  PV=P'V, 

where  P  and  Pr  are  the  pressures,  and  V  and  V  the  cor- 
responding volumes  of  a  given  quantity  of  gas,  kept  at  some 
fixed  temperature. 


MECHANICS   OF  GASES  81 

At  very  low  temperatures  or  at  very  high  pressures,  this 
law  of  Boyle  and  Mariotte  does  not  hold  exactly. 

It  should  be  noticed,  however,  that  the  air  in  a  bicycle 
pump  does  not  stay  at  the  same  temperature  when  com- 
pressed rapidly,  but  becomes  considerably  warmer.  The 
effect  of  this  heating  will  be  discussed  in  Chapter  X.  It 
will  then  appear  that  when  the  air  is  allowed  to  get  hot, 
more  work  has  to  be  done  on  the  pump  to  produce  the  same 
useful  result  on  the  tire.  The  same  is  true  of  large  com- 
pressors, and  so  it  is  customary  to  keep  the  air  in  them  as 
cool  as  possible  during  compression  by  circulating  water 
through  a  jacket  around  the  cylinder,  or  by  spraying  water 
into  the  cylinder.  The  ideal  case  is  compression  at  constant 
temperature,  in  accordance  with  Boyle's  law,  and  large  com- 
pressors should  come  as  near  to  this  as  is  practicable. 

PROBLEMS 

NOTE.  —Assume  constant  temperature  in  these  problems. 

1.  One  hundred  cubic  feet  of  air  under  a  pressure  of  15  pounds  per 
square  inch  is  compressed  to  300  pounds  per  square  inch.    What  does  the 
volume  become  ? 

2.  The  volume  of  a  tank  is  2  cubic  feet,  and  it  is  filled  with  com- 
pressed air  until  the  pressure  is  2000  pounds  per  square  inch.     How 
many  cubic  feet  of  air  under  a  normal  pressure  of  15  pounds  per  square 
inch  were  forced  into  the  tank  ? 

3.  What  is  the  total  force  applied  to  a  brake  piston  10  inches  in 
diameter,  when  the  pressure  is  80  pounds  per  square  inch? 

4.  One  hundred  cubic  feet  of  air  at  a  pressure  of  15  pounds  per  square 
inch  are  compressed  to  36  cubic  feet.     What  is  the  pressure  then? 

5.  Oxygen  is  sold  in  steel  tanks  under  a  pressure  of  150  pounds  per 
square   inch.     As   the   gas  is  used,  the  pressure  drops.     When  it  has 
dropped  to  50  pounds,  what  fractional  part  of  the  original  gas  remains? 
Give  your  reasoning. 

88.  Vacuum  pumps.  We  have  seen  how  a  bicycle  pump 
can  be  used  to  force  more  air  into  a  given  space,  and  now  we 
shall  see  how  a  slight  change  in  the  valves  will  enable  us  to 


PRACTICAL  PHYSICS 


suck  the  air  out  of  a  vessel.  The  first  of  these  so-called 
"  air  pumps "  was  made  as  long  ago  as  1650  by  a  German. 
Otto  von  Guericke,  then  mayor  of  Magdeburg,  who  per- 
formed numerous  experiments.  For  example,  he  found  that 
a  clock  in  a  vacuum  cannot  be  heard  to  strike;  a  flame  dies 
out  in  it ;  a  bird  opens  its  bill  wide,  gasps  for  air,  and  dies ; 
fish  perish ;  and  yet  grapes  can  be  preserved  six  months  in 
vacuo.  Vacuum  pumps  used  to  be  found  only  in  physical 

laboratories,  but  now  they  are 
used  so  extensively  in  vacuum 
cleaners,  and  in  making  in- 
candescent lamps  and  X-ray 
bulbs,  that  they  are  of  great 
commercial  importance. 

A  simple  form  of  mechan- 
ical vacuum  pump  is  shown 
in  figure  81.  It  consists  of  a 
metal  cylinder  O  fitted  with 
a  piston,  and  having  at  the 

lower  end  two  short  tubes,  A  and  jB,  within  which  are  self- 
acting  conical  valves,  so  arranged  that  the  air  enters  at  A 
and  leaves  through  B. 

When  the  piston  is  raised,  the  air  in  the  vessel  R,  which 
is  to  be  exhausted,  expands  into  the  cylinder  O  through  the 
valve  A.  When  the  piston  is  pushed  down,  it  compresses 
this  air,  closing  the  valve  A  and  opening  the  outlet  valve  B. 
Thus  with  each  double  stroke  a  certain  fraction  of  the  air  in 
the  vessel  R  is  removed.  It  will  be  seen  that  even  with  a 
mechanically  perfect  pump  we  never  take  out  quite  all  the 
air ;  for  by  each  stroke  we  remove  only  a  certain  fraction  of 
the  air,  and  the  remainder  expands  to  fill  the  vessel.  In 
practice,  no  pump  is  perfect  because  of  leakage.  To  reduce 
this,  it  is  common,  in  "high  vacuum"  pumps,  to  cover  the 
piston  arid  the  valves  with  oil,  and  in  some  forms  made  of 
glass  the  piston  is  replaced  by  a  column  of  mercury. 


FIG.  81.  —  Vacuum  pump. 


MECHANICS   OF  GASES 


83 


89.  Applications   of   the   vacuum   pump.     Vacuum  cleaning 
(Fig.  82)  is  an  application  of  the  force  of  suction,  created  by 
a  vacuum,  to  the  cleansing  of  buildings  and  their  furnishings. 
Some  vacuum  cleaners  are  portable 

and  some  are  stationary,  some  are 
operated  by  hand  and  some  by  an 
electric  motor,  some  tend  to  produce 
a  vacuum  by  a  pump  and  some  by  a 
rotating  fan,  but  the  general  prin- 
ciple is  the  same  in  all. 

The  problem  of  getting  the  air  out 
of  incandescent  lamp  bulbs  is  quite  dif- 
ferent from  that  of  vacuum  cleaning, 
in  that  we  have  a  very  limited  space 
to  be  exhausted  and  this  must  be 
very  completely  pumped  out.  Usually 
less  than  one  millionth  part  of  the 
air  is  left  in  the  bulb.  For  this 
purpose  two  mechanical  pumps  are 

worked  in  tandem,  one  to  take  air  directly  from  the  bulb, 
and  the  other  to  take  it  from  the  cylinder  of  the  first  pump. 
After  these  have  done  their  work,  the  air  remaining  is  still 
further  reduced  by  burning  phosphorus  or  some  other  com- 
bustible in  the  bulb.  X-ray  tubes  are  made  in  much  the 
same  way,  except  that  the  process  must  be  continued  longer 
so  as  to  produce  a  still  more  rarified  condition  of  the  air. 

WEIGHT  OF  THE  AIR 

90.  Density  of  air.     We  are  so  accustomed  to  having  air 
about  us  that  we  do  not  ordinarily  think    of  it  as  having 
either  volume  or  weight.     We  speak  of  an  "  empty  "  bottle 
when  we  usually  mean  a  bottle  filled  with  air.     Yet  when 
we  try  to  fill  a  narrow-necked  bottle  with  a  liquid,  we  find 
that  we  can  make  the  liquid  run  in  only  as  fast  as  the  air 
gets  out.     If  we  push  a  glass  tumbler  mouth  down  into  a 


FIG.  82.  —  Vacuum  cleaner. 


84  PRACTICAL  PHYSICS 

pail  of  water,  it  is  not  filled  with  water,  because  it  is  filled 
with  air.     Air  occupies  space  just  as  does  any  other  fluid. 

Furthermore,  air  and  other 
gases  have  weight,  although  we 
seldom  realize  this  fact. 

In  order  to  make  it  evident  that 
air  has  weight,  let  us  try  the  follow- 
ing experiments.  Suppose  we  care- 
fully counterbalance  on  the  scales 
(Fig.  83)  a  hollow  metal  vessel  (a  tin 
can  with  a  bicycle  valve  soldered  into 
the  top  will  serve).  Then  if  we 
pump  more  air  into  the  vessel  and 

FIG.  83.— Proof  that  air  has  weight,     put  it  on  the  scales  again,  we  find 

that  it  has  gained  in  weight.     If  we 

repeat  the  process,   we   find  that  it  weighs  a   little  more  after  each 

pumping. 

In  the  same  way  if  we  take  a  vessel  from  which  the  air  has  already 

been  exhausted,  such  as  an  electric  light  bulb,  carefully  counterbalance 

it,  and  then  let  the  air  in  by  filing  off  the  tip,  we  find  that  the  scalepan 

containing  the  bulb  and  the  broken  pieces  goes  down,  showing  that  the 

air  which  has  entered  has  weight. 

Careful  experiments  show  that  under  ordinary  conditions 
a  liter  of  air  weighs  about  1.3  grams,  or  1  cubic  foot  weighs 
about  1.3  ounces. 

Since  gases  have  both  volume  and  weight,  we  may  express 
their  densities  in  the  usual  way,  as  so  many  grams  per  cubic 
centimeter  or  so  many^  pounds  per  cubic  foot.  For  example, 
the  density  of  ordinary  air  is  about  0.0013  grains  per  cubic 
centimeter,  or  0.08  pounds  per  cubic  foot.  Many  gases  have 
densities  even  smaller  than  that  of  air.  Thus  the  density  of 
hydrogen  under  standard  conditions  is  only  0.000090  grams 
per  cubic  centimeter. 

Evidently  if  the  pressure  on  a  certain  volume  of  air  is 
doubled,  the  volume  is  halved,  and  the  air  becomes  twice  as 
dense.  In  other  words,  the  density  of  air  or  of  any  gas, 
varies  directly  as  the  pressure  at  constant  temperature. 


MECHANICS   OF  GASES  85 


PROBLEMS 

1.  If  a  liter  of  air  weighs  1.3  grams,  how  much  does  the  air  in  a  room 
weigh,  if  the  room  is  3  meters  high,  10  meters  long,  and  8  meters  wide? 

2.  If  the  pressure  in  a  compressed-air  tank  is  150  pounds  per  square 
inch,  what  does  1  cubic  foot  of  this  compressed  air  weigh  ?    (1  cubic  foot 
under  a  pressure  of  15  pounds  weighs  1.3  ounces.) 

3.  A  spherical  balloon  10  meters  in  diameter  is  filled  with  hydrogen. 
Find  the  weight  of  the  hydrogen. 

4.  A  bicycle  tire  has  about  the  same  volume  as  a  cylinder  85  inches 
long  and  1  inch  in  diameter.    If  you  pump  your  tires  up  from  15  pounds 
to  75  pounds  per  square  inch,  how  much  more  will  the  bicycle  weigh 
than  before? 

5.  A  compression  pump,  whose  capacity  is  500  cubic  centimeters,  is 
used  to  force  air  into  a  can  whose  volume  is  1  liter.    What  is  the  density 
of  the  air  after  3  complete  strokes? 

6.  A  vacuum  pump,  whose  capacity  is  500  cubic  centimeters,  is  used 
to  exhaust  the  air  from  a  liter  flask.     What  is  the  density  of  the  air  left 
in  the  flask  after  3  complete  strokes? 

91.  Pressure  of  the  atmosphere.  Since  we  are  living  at 
the  bottom  of  an  ocean  of  air,  and  this  air  is  a  fluid  which 
has  weight,  it  is  natural  to  expect  that  it  exerts  a  pressure. 
Ordinarily  we  are  not  aware  of  this  pressure  because  it 
pushes  up  on  the  bottoms  of  objects  almost  as  much  as  it 
pushes  down  on  the  tops  of  them.  If  we  could  get  rid  of 
this  upward  pressure  underneath,  we  would  see  how  great 
the  downward  pressure  on  top  really  is.  .  This  can  be  done 
with  a  vacuum  pump,  or  in  part 
even  with  the  lungs. 

Let  us  fasten  a  piece  of  sheet  rub- 
ber over  the  end  of  a  thistle  tube,  as 
shown  in  figure  84.  If  we  suck  the 
air  out  of  the  bulb  with  the  mouth, 
the  rubber  is  forced  downward  be-  FlG  84._RemoviDg  the  upward 
cause  of  the  atmospheric  pressure.  pressure  of  the  air. 

This  experiment  is  even  more  strik- 
ing when  performed  with  a  larger  membrane  and  with  a  vacuum  pump. 
If  we  tie  a  piece  of  rubber  over  the  mouth  of  the  glass  vessel  shown  in 


86 


PRACTICAL  PHYSICS 


figure  85,  and  gradually  pump  out  the  air,  the  rubber  will  be  pushed 
down  more  and  more  by  the  pressure  of  the  air  above  it,  until  it  finally 
bursts.  If  a  piece  of  bladder  is  used  instead  of  rubber,  it  will  break 
with  a  loud  report. 


FIG.  85.  —  Air  pressure  breaking  a  membrane.         FIG.  86.  —  Fountain  in  vacuo, 

If  we  pump  the  air  out  of  a  tall  glass  vessel  provided  with  a  stopcock 
and  jet  tube,  and  then  place  the  mouth  of  the  jet  tube  under  water 
and  open  the  stopcock,  we  see  the  water  rushing  up  into  the  vacuum 
like  a  fountain.  How  can  we  determine  how  much  air  was  removed  ? 

One  of  the  most  interesting  of  Otto  von  Guericke's  experi- 
ments was  that  with  his  famous  "Magdeburg  hemispheres." 
These  were  two  hollow  "hemispheres  a  little  over  a  foot  in 
diameter  which  fitted  together  so  well  that  the  air  could  be 
pumped  out  from  between  them.  The  pressure  of  the  sur- 
rounding atmosphere  then  held  them  together  firmly.  In  a 
test  before  the  Reichstag  and  the  Emperor,  it  required  six- 
teen horses,  four  pairs  on  each  hemisphere,  to  pull  them 
apart. 

92.  "Nature  abhors  a  vacuum."  The  ancients  tried  to 
explain  many  phenomena  by  saying  that  "nature  abhors  a 
vacuum,"  but  when  the  great  Italian  philosopher,  Galileo 
(1564-1642),  found  that  a  suction  pump  would  not  raise 


MECHANICS   OF  GASES 


87 


water  more  than  33  feet,  he  remarked  that  nature's  horror 
of  a  vacuum  was  a  curious  emotion  if  it  stopped  suddenly  at 
33  feet.  He  already  knew  both  that  air  has  weight  and  that 
the  "  resistance  to  a  vacuum  "  was  measured  by  a  column  of 
water  about  33  feet  high,  yet  he  left  it  to  his  friend  and 
successor,  Torricelli  (1608-1647),  to  unite  these  two  ideas. 
93.  Torricelli's  experiment.  Torricelli  devised  a  means  of 
measuring  this4' resistance"  which  nature  "offers  to  a  vacuum" 
by  a  column  of  mercury  in  a  glass  tube 
instead  of  a  column  of  water. 

We  may  repeat  this  experiment  if  we  take  a 
stout  glass  tube  about  3  feet  long,  closed  at  one 
end,  and  fill  it  completely  with  mercury.  If  we 
close  the  opening  with  the  finger,  invert  the  tube, 
and  put  its  open  end  into  a  tumbler  of  mer- 
cury, we  observe  that,  when  the  finger  is  removed, 
the  mercury  in  the  tube  (Fig.  87)  sinks  to  a  level 
about  30  inches  above  the  mercury  surface  in 
the  tumbler.  If  we  incline  the  tube  to  one  side, 
the  metal  fills  the  entire  tube  and  hits  the  top 
of  the  glass  with  a  sharp  click.  The  space  above 
the  mercury  is  empty  except  for  a  minute  quan- 
tity of  mercury  vapor.  It  is,  indeed,  the  most 
perfect  vacuum  that  we  know  how  to  make. 


FIG.  87.  —  Torricelli's 
experiment. 


The  column  of  mercury  in  the  tube 
just  balances  the  pressure  of  the  atmos- 
phere on  the  mercury  in  the  larger  vessel  at  the  bottom. 
In  other  words,  liquids  rise  in  exhausted  tubes  because  of 
the  pressure  exerted  by  the  atmosphere  on  the  surface  of  the 
liquid  outside,  and  not  because  of  any  mysterious  sucking 
power  created  by  the  vacuum. 

94.  How  to  calculate  the  pressure  of  the  atmosphere.  From 
the  law  that  pressure  in  a  heavy  liquid  is  everywhere  the 
same  at  the  same  depth,  we  know  that  the  pressure  on 
the  mercury  in  the  dish  (Fig.  88)  is  the  same  at  a  as 
outside. 


88 


PRACTICAL  PHYSICS 


Vacuum 


FIG.  88.  — Mercury 
column  supported 
by  air. 


Outside  this  pressure  is  exerted  by  the  atmosphere.  At  a 
it  is  exerted  by  the  column  of  mercury  ab.  Under  standard 
conditions,  the  pressure  at  a,  that  is,  the 
force  per  square  centimeter,  is  evidently 
equal  to  the  weight  of  a  column  of  mer- 
cury 76  centimeters  high  and  1  square  cen- 
timeter in  cross  section.  This  is  the  weight 
of  76  cubic  centimeters  of  mercury,  or  76 
times  13.6  grams,  or  1034  grams. 

In  the  English  system  it  is  the  weight 
of  a  column  of  mercury  about  30  inches 
high  and  1  square  inch  in  cross  section  ; 
that  is,  30  x  0.49,  or  14.7  pounds.  Roughly, 
then,  one  "  atmosphere  "  is  about  1  kilogram 
per  square,  centimeter  or  about  15  pounds 
per  square  inch. 

95.  Pascal's  experiments.  Pascal  reasoned 
that  if  the  mercury  column  was  held  up 
simply  by  the  pressure  of  the  air,  the  column  ought  to  be 
shorter  at  a  high  altitude.  So  he  carried  a  Torricelli  tube 
to  the  top  of  a  high  tower  in  Paris,  and  found  a  slight  fall 
in  the  height  of  the  mercury  column.  Desiring  more  de- 
cisive results,  he  wrote  to  his  brother-in-law  to  try  the 
experiment  on  the  Puy  de  Ddme,  a  high  mountain  in 
southern  France.  In  an  ascent  of  1000  meters,  the  mercury 
sank  about  8  centimeters,  which  greatly  delighted  and  as- 
tonished them  both. 

Pascal  also  tried  Torricelli's  experiment,  using  red  wine 
and  a  glass  tube  46  feet  long,  and  found  that  with  a 
lighter  liquid  a  much  higher  column  was  sustained  by  the 
pressure  of  the  air.  These  experiments  were  carried  out  in 
1648,  five  years  after  Torricelli's  discovery. 

96.  The  barometer.  The  arrangement  constructed  by 
Torricelli  may  be  set  up  permanently  as  a  means  of  measur- 
ing the  pressure  of  the  atmosphere.  It  is  then  called  a 


MECHANICS   OF  GASES 


89 


barometer.  To  "  read  the  barometer  "  means  simply  to  meas- 
ure accurately  the  height  of  the  mercury  column  above  the 
surface  of  the  liquid  in  the  reservoir.  In 
the  form  of  barometer  shown  in  figure  89 
this  reservoir  has  a  flexible  bottom  which 
may  be  raised  or  lowered  so  as  to  bring  the 
surface  of  the  mercury  to  the  zero  point  of 
the  scale  which  is  at  the  tip  of  a  point  pro- 
jecting into  the  reservoir.  The  height  of 
the  mercury  is  then  read  by  observing  the 
position  of  the  liquid  in  the  tube. 

A  more  convenient  form  to  carry  about 
is  the  aneroid  or  metallic  barometer  (Fig.  90). 
As  the  name  indicates,  it  is  "without 
liquid"  and  consists  essentially  of  a  disk- 
shaped  metal  box,  which  has  a  thin  corru- 
gated metal  top.  When  the  air  has  been 
pumped  out  of  the  box,  it  is  sealed  up,  its 
top  being  supported  by  a  stout  spring  to 
prevent  its  collapsing.  As  the  pressure  of 
the  air  changes,  the  top  of  the  box  moves 
up  or  down,  and  the  small  motion  is  greatly 
magnified  by  means  of  levers  and  a  delicate 
chain,  and  is  communicated  to  a  pointer 
which  moves  over  a  scale.  A  hairspring 
serves  to  take  up  the  slack  of  the  chain. 

The  scale  is  grad- 
uated to  corre- 
spond to  the  read- 
ings of  a  standard 
mercurial  barom- 
eter. Aneroid 
barometers  are  made  in  various 
sizes.  Some  are  even  as  small  as 

FIG.  90.  -  Aneroid  barometer.       Ordinary  watches. 


FIG.  89.  — Mercu- 
rial barometer. 


90 


PRACTICAL  PHYSICS 


97.  Uses  of  the  barometer.    The  barometer  indicates  changes 
in  atmospheric  pressure.     These  changes  may  be  due  to  fluc- 
tuations in  the  atmosphere 
itself  or  to  changes  in  the 
elevation  of  the  observer. 

If  a  barometer,  kept 
always  at  the  same  eleva- 
tion, is  frequently  observed, 
or  if  it  makes  a  continuous 
record,  as  does  a  barograph 
(Fig.  91),  it  is  found  to 

FIG.  91.  — Barograph,  or  self-recording        ;; 

barometer.  fluctuate  according  to   the 

weather.     Experience  shows 

that  a  "  falling  barometer,"  that  is,  a  sudden  decrease  of 
atmospheric  pressure, 
precedes  a  storm  ;  and  a 
"  rising  barometer,"  that 
is,  an  increasing  atmos- 
pheric pressure,  indi- 
cates the  approach  of 
fair  weather;  while  a 
steady  "  high  barom- 
eter" means  settled  fair 
weather. 

The  Weather  Bureau 
has  barometric  readings 
taken  simultaneously  at 
many  different  places, 
and  the  results  are  tele- 
graphed to  central  sta- 
tions, where  weather 
maps  are  prepared.  On 
these  maps  it  is  observed 


FIG.  92.  —  Portion  of  a  weather  map. 


that  there  are  certain  broad  areas  where  the  pressure  is  low, 
other  sections  where  the  pressure  is  high.     The  areas  of 


MECHANICS    OF    GASES  91 

low  barometric  pressure  are  usually  storm  centers,  which 
move  in  a  general  easterly  direction.  If  we  know  where 
these  low  pressure  areas  are  located  and  their  probable 
movement,  we  may  predict  the  weather.  Figure  92  shows 
a  portion  of  a  government  weather  map.  The  curved  lines, 
showing  the  places  where  the  barometric  pressure  is  equal, 
are  called  isobars.  The  direction  of  the  wind  at  places  of 
observation  is  indicated  by  an  arrow,  and  it  will  be  noticed 
that  these  arrows  usually  point  from  a  uhigh"  to  a  "low." 
A  careful  study  of  these  phenomena  (which  is  called  mete- 
orology) shows  that  these  "  lows  "  are  really  great  eddies  of 
air  slowly  moving  in  a  counterclockwise  direction  about 
the  center  of  the  low. 

Another  important  use  of  the  barometer  is  to  measure  the 
difference  in  altitude  of  two  places.  If  a  surveyor  or  explorer 
carries  a  barometer  up  a  mountain,  he  notices  that  it  indi- 
cates a  decrease  in  atmospheric  pressure  as  he  ascends.  For 
places  not  far  above  sea  level  this  decrease  is  about  1  milli- 
meter for  every  11  meters  of  elevation  or  0.1  of  an  inch  for 
every  90  feet  of  ascent.  Aneroid  barometers  graduated  in 
feet  or  meters  are  always  carried  by  balloonists  and  aviators 
to  tell  how  high  they  are. 

98.  Pressure  gauges.  Besides  barometers,  which  are  really 
pressure  gauges  designed  for  pressures  of  one  atmosphere  or 
less,  we  need  gauges  for  higher  pressures  such  as  those  in 
a  steam  boiler,  or  a  compressed-air  tank,  and  gauges  for  very 
low  pressures,  such  as  those  in  the  condenser  of  a  steam 
engine  or  a  vacuum  pump. 

To  measure  slight  diff  erences  in  pressure,  the  open  manometer, 
described  in  section  75,  is  used,  usually  with  some  liquid 
lighter  than  mercury  as  the  indicating  fluid. 

If  we  bend  a  piece  of  glass  tubing  as  shown  in  figure  93,  and  partly 
fill  the  tube  with  colored  water,  we  have  a  suitable  gauge  to  measure  the 
pressure  of  ordinary  illuminating  gas,  which  will  usually  cause  a  differ- 
ence in  levels,  A,  B,  of  about  2  inches. 


92 


PRACTICAL  PHYSICS 


For  high  pressures  this  form  of  gauge,  even  when  filled 
with  mercury,  becomes  too  cumbersome,  so  a  closed  manometer, 
like  that  shown  in  figure  94,  is  used.  The 
mercury  stands  at  the  same  level  in  both 
arms,  when  the  pressure  is  one  atmosphere. 
If  the  pressure  is  greater  than  this,  the 
mercury  is  forced  into  the  closed  arm,  com- 
pressing the  confined  air  according  to 
Boyle's  law.  The  scale  may  be  made  to 
read  in  atmospheres. 

For  practical  work,  the  Bourdon  spring 
gauge,  described  in  section  75,  is  used.  Such 
gauges  are  usually  graduated  so  as  to  read 
zero  when  the  pressure  is  really  one  atmos- 
phere ;  that  is,  they  indicate  the  difference 
between  the  given  pressure  and  atmos- 
pheric pressure.  Therefore  when  an  engi- 
FIG.  93.  —  Open  ma-  neer  speaks  of  a  pressure  of  100  pounds 
"  by  the  gauge,"  he  means  100  pounds  per 
square  inch  above  one  atmosphere ;  when  he  means  the  total 
pressure  above  a  vacuum,  he  usually 
says  "  100  pounds  absolute." 

When  pressures  less  than  one  atmos- 
phere are  to  be  measured,  such  as  the 
vacuum  in  the  condenser  of  a  steam  en- 
gine (section  219),  a  barometer  of  the 
ordinary  form  would  be  inconvenient 
because  the  whole  reservoir  or  cup  at 
the  bottom  would  have  to  be  exposed 
to  the  pressure  to  be  measured.  The 
gauge  is,  therefore,  arranged  so  as  to 
admit  the  low  pressure  to  be  measured 
to  the  top  of  the  barometer  tube.  The 
height  of  the  mercury  then  indicates  the  difference  between 
the  small  pressure  and  that  of  the  atmosphere.  The  better 


FIG.  94.  —Closed* manom- 
eter. 


MECHANICS   OF  GASES 


93 


the  vacuum,  the  higher  such  a  gauge  reads.  Thus  engi- 
neers usually  speak  of  a  26  or  a  28  inch  vacuum,  meaning 
a  pressure  less  than  the  standard  30  inch  atmosphere,  by  26 
or  28  inches  of  mercury.  The  best  vacuums  now  obtained 
steam  turbine  condensers  are  from  29  to  29.5  inches. 


in 


Since  these  mercury  gauges  would  be  inconvenient  in  engine 
houses,  Bourdon  gauges  are  used.  They  are  graduated  to 
read  in  inches  like  the  mercury  gauges  which  they  replace. 


PROBLEMS 


To  how 


Kerosene 


1.  A  diver  works  51  feet  below  the  surface  of  the  water, 
many  atmospheres  of  pressure  is  he  subjected  ? 

2.  When  the   barometer   reads  74.5  centimeters,  how  many  inches 
does  it  read?  • 

3.  When  a  mercury  barometer  reads  76  centimeters,  what  would  a 

glycerine  barometer  read  ?     (The  density  of  ^ ^ 

glycerine  is  1.26  grams  per  cubic  centimeter.) 

4.  When  the  barometer  reads  75  centi- 
meters,  what  is   the  atmospheric   pressure 
in  grams  per  square  centimeter? 

5.  During      a      storm     the      barometer 
"dropped"  1.5  inches.      How  far  would  a 
water  barometer  have  fallen  ? 

6.  If  a  certain  pressure  is  75  pounds  per 
square  inch,  how  many  kilograms  per  square 
centimeter  is  it  ? 

7.  During  a  mountain  climb  the  barom- 
eter falls   1.75   inches.      What  is   the   net 
height  climbed  (in  feet)  ? 

8.  Two  glass  tubes  are  arranged  verti- 
cally (Fig.  95)  so  that  their  lower  ends  dip 
into  water  and  kerosene,  respectively,  while 
their  upper  ends  are  joined  to  a  mouthpiece. 
When  some  of  the  air  in  the  tubes  is  sucked 
out,  the  water  rises  26  centimeters  and  the 
kerosene  33  centimeters.     Find  the  specific 
gravity  of  the  kerosene.     (This  is  a  common 
way  of  getting  specific  gravity.) 

9.  How  much  force  is  exerted  against  an  8-inch   piston  of  an  ah 
brake  when  the  pressure  is  90  pounds  "  by  the  gauge  "  ? 


Water 


FIG.  95.  —  Specific  gravity  by 
balanced  columns. 


94  PRACTICAL  PHYSICS 

10.  The  original  Magdeburg  hemispheres  are'  preserved  in  a  mu- 
seum at  Munich.  They  are  about  1.2  feet  in  diameter  inside.  When 
the  air  was  exhausted,  it  is  said  to  have  required  8  horses  on  each  half 
to  separate  them.  Assuming  that  the  pressure  of  the  atmosphere  was 
15  pounds  per  square  inch,  find  the  force  exerted  by  each  set  of  horses. 
(Reckon  pressure  on  circle  1.2  feet  in  diameter.  Why?) 

99.  The  lifting  effect  of  air.  We  have  seen  that  when  one 
climbs  a  mountain,  the  pressure  of  the  air  decreases.  A  sen- 
sitive barometer  will  indicate  this  decrease  of  pressure  even 
when  it  is  lifted  from  the  floor  to  a  table.  Therefore  the  up- 
ward pressure  of  the  air  on  the  bottom  of  any  object  is 
slightly  more  than  the  downward  pressure  of  the  air  on  the 
top.  In  other  words,  just  as  in  the  case  of  liquids,  there  is  a 
lifting  effect  on  everything  surrounded-  by  air,  and  this  lifting 

effect  is  equal  to  the   weight  of 
the  air  which  is  displaced. 


To  make  this  principle  of  the  buoy- 
ancy of  the  air  seem  more  real,  let  us 
balance  a  hollow  brass  globe  against  a 
solid  piece  of  brass  under  the  receiver  of 
a  vacuum  pump  (Fig.  96).  When  the 
air  is  pumped  out,  the  globe  seems  to  be 
heavier  than  the  solid  brass  weight,  be- 
cause the  support  of  the  air  around  it 
has  been  withdrawn.  If  the  air  is  re- 
admitted rapidly,  the  rise  of  the  globe 
FIG.  96.  —  Lifting  effect  of  air.  will  be  very  apparent. 

Most  things  are  so  heavy  in  comparison  with  the  amount 
of  air  they  displace  that  this  loss  in  weight,  due  to  the 
buoyancy  of  the  air,  is  not  taken  into  account.  For  example, 
a  barrel  of  flour  would  weigh  about  8  ounces  more  in  vacua 
than  in  air.  But  if  the  volume  of  air  displaced  is  very  large 
and  the  weight  small,  as  in  the  case  of  a  balloon,  the  object 
is  lifted  just  as  a  piece  of  wood  is  lifted  when  immersed  in 
water.  A  balloon  is  usually  made  of  cloth  which  is  treated 
with  a  special  varnish  to  make  it  as  nearly  gas-tight  as  possible, 


MECHANICS   OF  GASES 


95 


FIG.  97.  —  A  dirigible  balloon. 


and  is  surrounded  by  a  network  of  ropes  and  cords  to  hold 
up  the  car  and  its  load.  The  bag  is  filled  with  hydrogen, 
which,  volume  for  volume,  is  only  one  fourteenth  as  heavy 
as  air.  Sometimes,  for  short  trips,  illuminating  gas,  or  even 
hot  air  is  used.  Of  course  a  large  part  of  the  lifting  force  is 
used  in  raising  the  car,  the  rigging  of  the  balloon,  and  the 
silk  of  which  the  bag  is  made.  The  rest  is  available  for 
lifting  passengers  and  ballast.  To  compute  the  lifting  force 
of  a  balloon  we  have  only 
to  get  the  difference  between 
the  weight  of  the  air  dis- 
placed and  the  weight  of  the 
hydrogen,  gas,  or  hot  air. 

The  dirigible  balloon 
(Fig.  97)  is  provided  with 
propellers  driven  by  gas  engines,  and  rudders  to  steer  with. 
But  the  bag  has  to  be  made  so  large  to  support  the  weight 
of  all  this  machinery,  that  the  balloon  is  much  at  the  mercy 
of  the  wind. 

100.  Pumps  for  liquids.  The  ancients 
used  pumps  to  lift  water  from  wells,  even 
though  they  did  not  know  why  a  pump 
works ;  they  thought  it  was  because  "  na- 
ture abhors  a  vacuum."  We  know  now 
that  the  underlying  principle  is  the  same 
as  in  a  mercurial  barometer :  it  is  the 
pressure  of  the  atmosphere  on  the  surface 
of  the  water  in  the  well  that  pushes  the 
water  up  into  the  pump. 

For  example,  let  us  consider  the  ordi- 
nary suction  pump  shown  in  figure  98. 
This  consists  of  a  cylinder  (7,  which  is 
connected  with  the  well  or  cistern  by  a 
pipe  T.  At  the  bottom  of  the  cylinder  is 

FIG.  98.  —  A  suction  J 

pump.  a  clapper  valve  o,  opening  up.     A  piston 


96 


PRACTICAL   PHYSICS 


P  can  be  worked  up  and  down  in  the  cylinder  by  means 
of  a  handle.  This  piston  also  contains  a  valve  opening 
up.  On  the  up  stroke  of  the  piston  P,  the  valve  V  remains 
closed  because  of  its  weight  and  the  pressure  of  the  air  upon 
it.  Between  the  piston  and  the  bottom  of  the  cylinder  there 
would  be  a  partial  vacuum  if  the  valve  S  remained  closed. 
But  the  pressure  of  the  air  on  the  water  in  the  well  forces 
some  water  up  through  the  pipe  T,  past  the  valve  S  into  the 
cylinder  (7.  On  the  down  stroke  of  the  piston  the  valve  S 
closes,  the  valve  V  opens,  and  the  water  gets  above  the 
piston.  On  the  next  up  stroke  it  is  lifted  out  through  the 

spout.  The  valve  S  must  never 
be  more  than  34  feet  above  the 
water  in  the  well,  and  in  practice 
this  distance  is  seldom  more  than 
30  feet.  Why? 

Another  kind  of  pump,  shown 
in  figure  99,  is  called  a  force  pump. 
The  suction  pipe  T  with  its  valve 
S  are  exactly  like  the  correspond- 
ing parts  of  the  house  pump  just 
described,  but  the  piston  has  no 
opening  through  it,  and  the  outlet 
pipe  and  a  second  valve  are  at  the 
bottom  of  the  cylinder.  Rais- 
ing the  piston  fills  the  cylinder 
with  water  ;  pushing  it  down 
again  forces  the  water  out  through 
the  second  pipe.  If  enough  force 
is  exerted  on  the  piston,  the  water 
can  be  pushed  up  to  a  considerable  height.  The  pump  can 
therefore  be  located  near  the  bottom  of  a  well  or  mine 
shaft. 

Since  the  water  is  forced  up  only  on  the  down  stroke,  it 
comes  in  jerks.     To  reduce  the  jar  and  shock,  an  air  chamber 


FIG.  99,  —  A  force  pump. 


MECHANICS   OF  GASES 


97 


ivery 


A  is  connected  with  the  delivery  pipe,  so  that  the  air  may  act 
as  a  cushion  or  spring.  Power  pumps,  such  as  are  used  on 
fire  engines,  or  in  city  waterworks, 
are  "  double  acting "  (Fig.  100), 
which  gives  a  still  steadier  stream. 
When  a  large  volume  of  water  is 
to  be  lifted  a  short  distance,  a  cen- 
trifugal pump  (Fig.  101)  is  used. 
This  is  something  like  a  water  wheel 
worked  backwards.  As  the  wheel  in- 
side (Fig.  102)  is  turned,  the  water, 
which  enters  near  the  hub,  gets 
caught  between  the  blades  and  is 
hurled  outward  into  the  delivery 
space  around  the  wheel,  even  against 
some  pressure  there.  Similar  ma- 
chines, called  "  blowers,"  are  used  to  FlG-  m'~  A  double-acting 

£  »     .     ,,  ,        ,      .,,  force  pump. 

force  a  current  of  air  through  a  build- 
ing for  ventilation,  or  to  make  "  f 6rced 
draft,"  for  furnaces.  Often  several 
of  these  pumps  are  used  in  series  to 
give  higher  pressures.  Large  tur- 
bine pumps  of  this  sort,  driven  by 
steam  turbines,  have  recently  begun 
to  revolutionize 
blast  furnace 
practice  in  the 
United  States, 

FIG.  101. -Centrifugal  pump.    because    of     the 

extremely   steady   rate   at  which   they 

furnish  the  air  needed  for  combustion. 

Another  form  of  pump  is  the  "  air-lift " 

pump  (Fig.  103).     Its   action   depends 

upon    the    formation    of   a    column   of  . 
\       ,  7.1.1  i.    FlG-  102-  —  Section  of  cen* 

mixed  water  and  aw  which,  because  of  trifugai  pump. 


98 


PRACTICAL  PHYSICS 


JVatcr 


its  lesser  specific  gravity,  is  raised  by  a  shorter  column  of 

water.     Such  a  pump  will  lift  water  mixed  with  air  as  much 
compressed  as  40  feet  above  the  level  of  the  water.     It  con- 

sists of  two  tubes,  the  smaller  of  which  is 
centered  within  the  larger.  The  smaller  pipe 
conveys  compressed  air  down  into  the  water  to 
be  lifted.  The  mixture  of  water  and  air  rises 
through  the  outer  tube.  This  sort  of  pump 
is  cheap  to  make,  is  simple  in  its  operation,  and 
has  no  wearing  parts  ;  but  its  efficiency  is  low. 
It  would  be  especially  useful  in  an  artesian  or 
oil  well  if  the  water  or  oil  naturally  stands  too 
far  below  the  surface  to  be  reached  by  a  suction 
pump  and  if  the  well  is  so  small  that  a  force 
pump  cannot  be  put  down  into-  it. 

101.  Siphon.  The  siphon  is  a  bent  tube  with 
unequal  arms.  It  is  used  to  empty  bottles  and 
tanks  which  cannot  be  overturned,  or  to  draw 
off  the  liquid  from  a  vessel 
without  disturbing  the  sedi- 
ment at  the  bottom.  If  the 
tube  is  filled  and  placed  in  the 
position  shown  in  figure  104, 
the  liquid  will  flow  out  of  the 
vessel  A  and  be  discharged  at 
a  lower  level  D.  The  force 

which   makes  it  flow  is  the  weight  of   the 

column  of  water  <7Z),  which  is  between  the 

water  level  A  A'  and  the  water  level  DDf. 

If  the  water  level  DDf  is  raised  to  AA1 ',  this 

moving  force  becomes  nothing  and  the  water 

ceases  to  flow  ;    if   the  level  DDf  is  lifted 

above  AA' ,  the  liquid  flows  back   into  the 

vessel  A.     A  siphon  works,  then,  as  long  as  the  free  surface 

of  the  liquid  in  one  vessel  is  lower  than  the  free  surface  of 


FIG.  103.  — Air- 
lift pump. 


FIG.   104. —A 
siphon. 


MECHANICS   OF  GASES  99 

the  liquid  in  the  other  vessel.  A  water  siphon  will  not 
work  if  the  top  of  the  bend  B  is  more  than  34  feet  above 
the  level^'.  Why? 

Siphons  are  often  used  on  a  large  scale  in  engineering. 
For  instance,  in  power  plants  the  water  used  to  condense  the 
steam  is  often  taken  from  the  ocean,  raised  10  or  15  feet  to 
the  condenser,  and  carried  back  to  the  ocean,  through  a  pipe 
that  is  everywhere  air-tight  and  acts  like  a  siphon.  The  only 
work  that  the  pumps  have  to  do  is  to  keep  the  water  moving 
against  the  friction  in  the  pipe.  A  large  inverted  siphon  is 
used  at  Storm  King  on  the  Hudson  River,  to  carry  the  water 
supply  of  New  York  City  under  the  river,  some  700  feet  below 
its  surface.  The  lifting  of  the  water  on  one  side  is  done  by 
the  water  descending  from  a  slightly  greater  height  on  the  other. 

Siphons  on  a  smaller  scale  are  used  in  every  aqueduct  to 
carry  water  over  hills  or  across  valleys.  In  such  cases  air 
bubbles  carried  along  in  the  water  tend  to  collect  at  the  top 
of  every  hill,  and  so  small  air  pumps  have  to  be  installed  to 
keep  the  pipes  full  of  water. 

PROBLEMS 

1.  How  many  feet  could  water  be  lifted  with  a  perfect  suction  pump 
(a)  at  sea  level,  and  (6)  in  Denver,  Col.  (altitude  about  5000  ft.)  ? 

2.  How  many  feet  could  crude  oil  (density  0.89  grams  per  cubic  centi- 
meter) be  lifted  out  of  an  oil  well  by  a  perfect  suction  pump  at  sea  level  ? 

3.  How  much  work  is  needed  to  lift  100  gallons  of  water  25  feet 
with  a  perfect  pump  ? 

4.  How  much   power   is  needed  to  raise   100  gallons  of    water  per 
minute  25  feet  with  a  perfect  pump? 

5.  A  force  pump  is  to  deliver  water  at  a  point  20  feet  above  the  level 
of  its  barrel.     How  great  is  the  water  pressure  in  the  barrel  when  the 
piston  is  descending  ? 

6.  The  piston  of  a  fire-engine  force  pump  is  4  inches  in  diameter,  and 
the  total  force  exerted  on  it  by  the  engine  is  600  pounds.     If  the  pump 
acts  perfectly,  at  how  great  a  height  will  it  deliver  water  ? 

7.  A  siphon  is  to  be  used  to  transfer  mercury  from  one  bottle  to 
another.     How  far  above  the  level  of  the  mercury  in  the  higher  bottle 
can  the  top  of  the  siphon  tube  be? 


100  PRACTICAL  PHYSICS 

OTHER  LESS  IMPORTANT  PROPERTIES  OF  GASES 

102.  Absorption  of  gases  in  liquids.    If  we  slowly  heat  a  beakei 
containing  cold  water,  small  bubbles  of    air  will  be  seen  to  collect  in 
great  numbers  upon  the  walls  (Fig.  105)  and  to  rise  through  the  liquid 

to  the  surface.  It  might  seem  at  first  that  these  are 
bubbles  of  steam,  but  they  must  be  bubbles  of  air,  first 
because  they  are  formed  at  a  temperature  below  the 
boiling  point  of  water,  and  second  because  they  do  not 
condense  .as  they  come  to  the  cooler  layers  of  water 
above. 

This  simple  experiment  shows  that  ordinary 
water  contains  dissolved  air,  and  that  the 
amount  of  air  which  water  can  hold  decreases 
FIG.  105.  —  Bub-  as  the  temperature  rises.  It  is  the  oxygen  of 
bies  of  air  in  the  air  that  is  dissolved  in  water  which  sup- 
ports the  life  of  fish.  The  amount  of  gas  ab- 
sorbed by  a  liquid  depends  on  the  pressure  of  the  gas  above 
the  liquid.  Thus  soda  water  is  oidinary  water  which  has 
been  made  to  absorb  large  quantities  of  carbon  dioxide 
gas  by  pressure.  When  the  pressure  is  relieved,  the  gas 
escapes  in  bubbles,  causing  effervescence.  Careful  experi- 
ments show  that  the  amount  of  gas  absorbed  is  proportional 
to  the  pressure.  The  amount  of  gas  which  will  be  absorbed 
by  water  varies  greatly  with  the  nature  of  the  gas.  For 
example,  at  0°  C.  and  at  a  gas  pressure  of  76  centimeters  of 
mercury,  1  cubic  centimeter  of  water  will  absorb  0.049  cubic 
centimeters  of  oxygen,  1.71  cubic  centimeters  of  carbon  di- 
oxide, and  1300  cubic  centimeters  of  ammonia  gas.  The 
ordinary  commercial  aqua  ammonia  is  simply  ammonia  gas 
dissolved  in  water. 

103.  Absorption  of  gases  in  solids.     Certain  porous  solids, 
such  as  charcoal,  meerschaum,  silk,  etc.,  have  a  great  capacity 
for  absorbing  gases.     For  example,  charcoal  will  absorb  90 
times  its  volume  of  ammonia  gas  and  35  volumes  of  carbon 
dioxide.     It  is  this  property  of  charcoal  which  makes  it  use- 


MECHANICS   OF  GASES 


101 


ful  as  a  deodorizer.  This  absorption  seems  to  be  due  to  the 
condensation  of  a  layer  of  gas  on  the  surface  of  the  body  or 
of  the  pores  within  the  body.  Platinum  in  a  spongy  state 
absorbs  hydrogen  gas  so  powerfully  that  if  a  small  piece  is 
placed  in  an  escaping  jet  of  hydrogen,  the  heat  developed 
by  the  condensation  is  enough  to  ignite  the  jet.  This  has 
been  made  use  of  in  self-lighting  Welsbach  mantles. 

A  familiar  example  of  the  absorption  of  gases  by  liquids 
and  solids  is  the  contamination  of  milk  and  butter  by  onions, 
fish,  or  other  kinds  of  food,  if  they  are  kept  in  the  same  com- 
partment of  a  refrigerator.  Onions,  for  instance,  give  off  a 
small  quantity  of  gas  which  we  can  easily  detect  by  our 
sense  of  smell,  or  by  the  watering  of  our  eyes.  This  gas, 
when  absorbed  by  milk  or  butter,  affects  its  taste. 

104.  Diffusion  of  gases.  One  of  the  difficulties  in  the  suc- 
cessful construction  of  balloons  is  due  to  the  diffusion  of  the 
gas  through  the  bag.  The  diffusion  of 
hydrogen  through  a  porous  cup  is 
shown  in  the  following  experiment. 

If  we  set  up  a  porous  cup  with  a  stopper 
and  glass  tube,  as  shown  in  figure  106,  and 
allow  hydrogen  (or  illuminating  gas)  to  fill  the 
jar  which  surrounds  the  porous  cup,  we  observe 
bubbles  rising  from  the  end  of  the  glass  tube, 
which  dips  underwater.  This  means  that  the 
gas  is  going  through  the  porous  walls  of  the 
cup  and  forcing  the  air  out  at  the  bottom. 
If  we  now  shut  off  the  gas  and  remove  the  jar, 
we  presently  see  the  water  slowly  rising  in  the 
tube,  which  shows  that  the  gas  inside  the  cup 
is  going  out. 


FIG.  106.  — Diffusion  of 
hydrogen  through 
porous  cup. 


The  fact  that  a  little  ammonia  (or 
any  other  gas  with  a  powerful  odor) 
introduced  into  a  room  is  soon  perceptible  in  every  part  of 
the  room  shows  that  the  gas  particles  travel  quickly  across 
the  room.  Moreover,  this  mixing  of  gases  goes  on  whatever 


102  PRACTICAL   PHYSICS 

the  relative  densities  of  the  gases,  so  that  a  heavy  gas  like 
carbon  dioxide  and  a  light  gas  like  hydrogen  will  not  re- 
main  in  layers  like  mercury  and  water,  but  will  quickly 
diffuse  and  become  a  homogeneous  mixture.  Experiments 
show  that  the  smaller  the  density  of  the  gas,  the  greater 
the  velocity  of  its  diffusion. 

105.  Molecular  theory  of  gases.  To  explain  the  pressure 
of  gases  and  their  diffusion,  it  is  now  generally  supposed  that 
all  substances  are  made  of  very  minute  particles  called 
molecules.  These  molecules  are  so  minute  that  we  cannot  see 
them  even  with  the  most  powerful  microscopes.  In  one  cubic 
centimeter  of  a  gas  there  are  probably  not  less  than  1019 
(that  is,  1  followed  by  nineteen  ciphers)  molecules.  The 
spaces  between  these  molecules  are  supposed  to  be  much 
larger  than  the  molecules  themselves.  This  explains  why 
gases  are  so  easily  compressed  and  diffuse  so  quickly. 

Then,  too,  these  little  particles  are  supposed  to  be  flying 
about  in  all  directions  with  great  velocity.  They  are  sup- 
posed to  travel  in  straight  lines  except  when  they  hit  each 
other  and  bounce  off.  Gas  molecules  seem  to  have  no  inher- 
ent tendency  to  stay  in  one  place,  as  do  the  molecules  of  solids. 
This  explains  why  gases  fill  the  whole  interior  of  a  contain- 
ing vessel.  This  also  explains  gas  pressures,  for  the  blows 
which  the  innumerable  molecules  of  a  gas  strike  against  the 
surrounding  walls  constitute  a  continuous  force  tending  to 
push  out  these  walls.  When  a  gas  is  compressed  to  half  its 
volume,  the  pressure  is  doubled,  because  doubling  the  density 
doubles  the  number  of  blows  struck  per  second  against  the 
walls.  It  has  even  been  possible  to  calculate  the  molecular 
velocity  necessary  to  produce  this  outward  pressure.  It  ap- 
pears that  the  molecules  of  gases  under  ordinary  conditions 
are  traveling  at  speeds  between  1  and  7  miles  per  second. 
The  speed  of  a  cannon  ball  is  seldom  greater  than  one  half  a 
mile  per  second. 

This,  in  brief,  is  the  so-called  kinetic  theory  of  gases. 


MECHANICS   OF  GASES  103 

SUMMARY   OF  PRINCIPLES   IN   CHAPTER  IV 

Pascal's  Law  of  Transmission  of  Pressure :  For  gases  under 
pressure,  the  pressure  is  everywhere  the  same ;  the  force  varies 
as  the  area. 

Boyle's  Law :  Volume  of  gas  at  constant  temperature  varies  inversely 
as  pressure. 

Density  of  a  gas  varies  directly  as  pressure. 

Lifting  effect  of  air  is  equal  to  weight  of  air  displaced. 

Atmospheric  pressure  equal  to  about 
30  inches  of  mercury, 
34  feet  of  water, 
15  pounds  per  square  inch, 
1  kilogram  per  square  centimeter. 


QUESTIONS 

1.  Why  can  Torricelli's  experiment  be  performed  as  well  indoors  as 
outdoors  ? 

2.  How  and  why  can  a  glass  of  water  be  inverted  with  the  aid  of  a 
card  without  spilling  the  water  ? 

3.  Why  does  a  rubber  tube  often  collapse  when  connected  with  a 
vacuum  pump?     Why  does  not  a  rubber  tube  always  collapse  when  con- 
nected with  a  vacuum  pump? 

4.  Why  must  a  mercurial  barometer  be  hung  in  a  vertical  position  ? 

5.  What  would  be  the  result  of  putting  a  mercurial  barometer  under 
a  tall  bell  glass  on  an  air  pump  ? 

6.  Would  a  siphon  work  in  a  vacuum  ? 

7.  What  would  be  the  effect  of  lengthening  the  long  arm  of  a  si- 
phon ? 

8.  A  boat  lying  on  a  beach  is  full  of  water.     How  could  you  empty 
it  with  the  help  of  a  suitable  length  of  rubber  hose  ?     Could  you  use  the 
same  method  to  get  the  bilge  water  out.  of  a  boat  floating  in  the  water  ? 

9.  Why  are  not  barometers  filled  with  water  ? 

10.   What  advantage  has  a  pneumatic    automobile  tire  over  a  solid 
tire  of  the  same  size  ? 


104 


PRACTICAL  PHYSICS 


11.  How  can  a  balloon  be  made  to  sink  or  rise  ? 

12.  Why  does  a  man  under  water  in  a  diving  suit  have  to  be  sup- 

plied with  compressed  air? 

13.  Explain  why  the  liquid  does  not  run  out  of 
a  medicine  dropper. 

14.  Explain  the   action   of   a  so-called  "pneu- 
matic "  inkstand  (Fig.  107),  or  of  a  drinking  foun- 
tain (Fig.  108),  or  of  a  poultry  fountain  (Fig.  109). 

15.  A  man  finds  that  cider  does  not  flow  out  of 
a  barrel  until  he  removes  the  bung.     Explain. 

16.  A  vessel  1  meter  deep  is  filled  with  mercury. 
Can  it  be  entirely  emptied  by  means  of  a  siphon? 

17.  Why  does  a  chemist  usually  reduce  the  vol- 
umes of  gases   to   standard  pressure,  that   is,   76 
centimeters? 

18.  What  advantages  has  compressed  air  over 
electricity  for  the  transmission  of  power? 

19.  If  the  area  of  a  man's  body  is  20  square 
feet,  what  is  the  total  force  exerted  on  him  by  the 
atmosphere?     Why  is    he    not    crushed    by    this 
force  ? 

20.  What  facts  indicate  that  the  atmosphere  be- 
comes rarer  and  rarer  as  one  rises  above  sea  level  ? 

21.  In  building  tunnels  workmen  usually  »have 
to  work  in  chambers  filled  with  compressed   air. 
Why  is  this  necessary  ? 

22.  Get  the  dimensions   and  weights   of   some 

of  the  large  balloons  used  in  international  races,  and  compute  their 
lifting  power.  Estimate  the  amount  of  ballast 
that  can  be  carried  in  addition  to  the  weight 
of  the  balloon,  car,  and  passengers. 

23.  How  does  a  gas  meter  work  ? 

24.  Would  it  make  any  difference  in  the 
gas  bill  if  the  meter  were  in  the  attic  instead 
of  in  the  cellar?     In  apartment  houses  with 
separate   meters  for  each  apartment,   do  the 
people  on  the  top  floor  get  more  or  less  gas 
for  their  money? 


FIG. 


108.  —  Drinking 
fountain. 


FIG. 


109.  —  Poultry  foun- 
tain. 


CHAPTER  V 


NON-PARALLEL   FORCES 

Representation  of  forces  by  arrows  —  the  parallelogram  of 
forces  —  composition  and  resolution  of  forces  —  application  to 
roof  truss,  friction,  sailboat,  and  aeroplane. 

106.  Three  forces  acting  at  a  point.     In  machines  and  other 
contrivances  it  often  happens  that  forces  which  are  not  par- 
allel balance  each  other  and  are  thus  in  equilibrium.     For 
example,  suppose  a  street 

lamp  is  suspended  over  a  A 
street  by  a  wire  stretched 
between  two  posts,  as 
shown  in  figure  110. 
We  have  here  three  non- 
parallel  forces  in  equilib- 
rium —  first,  the  verti- 
cal pull  OW  due  to  the 
weight  of  the  lamp;  sec- 
ond, the  pull  exerted  by  one  of  the  ropes ;  arid  third,  the 
pull  exerted  by  the  other  rope.  We  are  to  find  what  relation 
must  exist  between  the  magnitude  and  direction  of  any  three 
such  forces,  if  they  are  to  produce  equilibrium. 

107.  Representation  of  forces  by  arrows.     It  will  help  us  to 
form  a  mental  picture  of  these  three  forces  if  we  represent 
them  by  three  arrows.     The  direction  of  each  force  will  be 
indicated  by  the  direction  of  the  arrow,  the  point  of  applica- 
tion by  the  tail  of  the  arrow,  and  the  magnitude  of  the  force 
by  the  length  of  the  arrow,  drawn  to  some  convenient  scale. 

105 


FIG.  110.  — Three  non-parallel  forces. 


106 


PRACTICAL  PHYSICS 


Thus  in  figure  111  we  have  an  arrow  5  units  long,  and  if  we 

assume  that  each  unit  represents  10  pounds,  the  arrow  AB 

,     ,     .     ,     ,   v        shows  a  force  of  50  pounds  applied  at  A, 

acting  due  east.     Figure  112  represents 

FIG.  111.- A  force  of  50     t         f  QA     f  3Q  poundg         ti 

pounds  acting  east. 

due  east  applied  at  0,  and  the  other  OB 
of  40  pounds,  acting  due  north,  applied  at  the  same  point  0. 

If  these  two  forces  act  simultaneously  upon  the  body  at  0, 
the  result  will  be  the  same  as  if  a  single  force  were  applied, 
acting  somewhere  between  OA  and  OB, 
but  nearer  the  greater  force  OB.  This 
single  force,  which  produces  the  same  result 
as  two  forces,  OB  and  OA,  is  called  their 
resultant. 

108.  Principle  of  parallelogram  of  forces. 
If  a  parallelogram  is  constructed  on  OA  and 
OB,  the  diagonal  00  represents  the  resultant, 
as  can  be  proved  by  the  following  experi- 
ment. 


Suppose  we  hang  two  spring 
balances  A  and  B  from  two  nails 
in  the  molding  at  the  top  of  the 
blackboard,  as  shown  in  figure 
113,  and  tie  some  known  weight 
W  near  the  middle  of  a  string 
joining  the  hooks  of  the  two 
balances.  If  we  draw  lines  on 
the  blackboard  behind  each  of 
the  three  strings,  we  shall  have 
represented  the  direction  of  each 
of  the  three  forces.  Then,  if  we 
note  the  tension  in  each  string 
as  shown  by  the  amount  of  the 
weight  W  and  the  readings  of 
the  spring  balances  A  and  B,  we 
may  remove  the  apparatus  and 
FIG.  113.  —  Experiment  to  illustrate  paral-  complete  the  diagram.  Choos- 


lelogram  law. 


ing  some  convenient  scale,  we 


NON-PARALLEL   FORCES  107 

measure  off  on  OA  a  distance  corresponding  to  the  tension  in  OA,  and 
place  an  arrowhead  at  X ,  and  in  the  same  way  we  locate  Y  on  OB.  Then 
we  construct  a  parallelogram  on  OX  and  OF  by  drawing  XR  parallel  to 
OF  and  YR  parallel  to  OX.  It  will  be  evident  that  the  diagonal  OR  is 
the  resultant  of  OX  and  OF,  for  if  we  measure  OR  and  determine  its 
magnitude  from  our  scale  of  force,  we  find  that  this  resultant  OR  is 
almost  exactly. equal  and  opposite  to  the  third  force  OW.  That  is,  either 
OR,  or  OX  and  OF,  balances  OW. 

The  force  necessary  to  balance  or  hold  in  equilibrium  two 
forces  is  called  the  equilibrant.  Thus  in  the  case  just  de- 
scribed, the  force  OWis  the  equilibrant  of  the  two  forces  OX 
and  OY. 

The  resultant  of  two  forces  acting  at  any  angle  may  be  rep- 
resented by  the  diagonal  of  a  parallelogram  constructed  on  two 
arrows  representing  the  two  forces. 

When  three  forces  are  in  equilibrium,  the  resultant  of  any 
two  of  the  forces  is  equal  and  opposite  to  the  third,  which  can 
be  regarded  as  their  equilibrant. 

109.  Resultant  depends  on  the  angle  between  components. 
To  determine  the  resultant  of  two  or  more  forces,  we  must 
know  not  only  the  magnitude  of  the  "  components,"  but  also 
the  angle  between  them.  This  will  be  made  clear  by  study- 
ing the  same  two  forces  at  different  angles,  as  in  figure  114. 
It  will  be  seen  that  the  resultant  OR  gradually  increases  as 


O       4.       "  O 

(c)  (d)  (e) 

FIG.  114.  —  Two  forces  at  varying  angles. 

the  angle  between  the  components  OA  and  OB  decreases. 
For  example,  if  the  angle  is  180°  (case  (a)),  the  forces  OA 
and  OB  are  opposite  and  the  resultant  is  the  difference  be- 
tween the  forces,  4  —  3,  or  1,  and  acts  in  the  direction  of  the 
greater  force,  i.e.  toward  the  right.  As  the  angle  gradually 
decreases  the  resultant  OR  increases,  until,  when  the  angle  is 


108 


PBACTICAL  PHYSICS 


0°  (case  (e)),  the  forces  OA  and  OB  are  acting  in  the  same 
straight  line  and  in  the  same  direction,  and  the  resultant  is 
the  sum  of  the  two  forces,  4  +  3,  or  7.  When  the  forces  are 
at  right  angles  (case  (<?))»  the  resultant  can  be  computed  from 
the  geometrical  proposition  about  the  sides  of  a  right  triangle, 
namely,  the  square  on  the  hypothenuse  is  equal  to  the  sum  of  the 
squares  on  the  two  sides. 

OX?  =  'OA2  +  ~0&, 
-       =  32  +  42  =  25, 


Thus, 


OR  =  5. 


For  oblique  angles,  such  as  (5)  and  (c?)  in  figure  114,  the 
resultant  can  be  determined  by  plotting  the  forces  to  scale, 
or  by  trigonometryc 

The  process  of  finding  the  resultant  of  two  or  more  com- 
ponent forces  is  called  the  composition  of  forces. 

110.  Composition  of  forces.  —  Illustrative  Examples.  Suppose 
we  have  a  crane  arm  AE,  attached  to  the  wall  as  shown  in  figure  115  (a). 

E  The  weight  Wis  2000  pounds  and 
the  tension  in  the  cable  A  C  is  1500 
pounds.  What  is  the  force  exerted 
by  ABt  In  the  solution  of  such 
problems  it  will  be  found  helpful 
to  draw  a  force  diagram  (Fig.  115 
(6)),  where  A  W  represents  the 
pull  of  the  weight  W,  A  C  the  pull 
of  the  cable,  and  A  E  the  thrust 
of  the  crane  arm.  As  these  three 
forces  are  in  equilibrium,  we  can 
apply  the  principle  of  the  parallel- 
ogram of  forces.  We  want  to 
find  AR,  the  resultant  of  A  C  and 
A  W.  Since  A  C  and  A  W  form  a 
Fia.  115.  —  Three  forces  acting  on  crane,  right  angle,  we  know  that 


Zft2  =  ZC2  +  ZTP2  =  I5002  +  20002, 
or  A£  =  2500  pounds. 

Therefore  the  push  exerted  by  AB  is  2500  pounds. 


NON-PARALLEL   FORCES 


109 


Again,  suppose  we  have  a  100-pound  child  in  a  swing  (Fig.  116). 
A  man  pushes  the  child  to  one  side  with  a 
force  of  20  pounds.  What  is  the  magnitude 
and  direction  of  the  pull  exerted  by  the 
rope?  In  the  force  diagram  (Fig.  116), 
CW  represents  the  weight  of  the  child 
(100  pounds),  CP  represents  the  push 
(20  pounds)  of  the  man  against  the  child, 
and  CR  represents  the  pull  of  the  rope 
which  we  wish  to  determine.  The  re- 
sultant CR'  of  CP  and  CW  is  equal  to 
CW2,  or  V(20)2+  (100)2,  or  about 


102  pounds.  Therefore  the  tension  in  the 
rope  is  also  102  pounds.  Its  direction  can 
be  found  from  the  diagram. 

PROBLEMS  FlG  116  _  Three  forces  acting 

1.  Find,  by  plotting  to  scale,  the  result-  on  child  in  swing' 

ant  of  a  force  of  8  pounds  toward  the  east,  and  one  of  4  pounds  toward 
the  north. 

2.  Compute  the  resultant  in  problem  1. 

3.  A  force  of   100  pounds  acts  north  and  an  equal  force  acts  west. 
What  is  the  direction  and  magnitude  of  the  equilibrant? 

4.  Find  the  resultant  of  a  force  of  10  pounds  east  and  one  of  14  pounds 
southwest. 

5.  Two  forces,  5  pounds  and  12  pounds,  act  at  the  same  point.     Find 
their  equilibrant,  (a)  if  they  act  in  the  same  direction,  (ft)  if  they  act  in 
opposite  directions,  and  (c)  if  they  act  at  right  angles. 

111.  Resolution  of  forces.  The  principle  of  the  composi- 
tion of  forces  can  be  worked  backward.  If  one  force  is 
given,  we  can  find  two  others  in  given  directions  which  will 
balance  it.  For  example,  take  the  case  of  the  lamp  sus- 
pended above  the  middle  of  the  street.  If  we  know  the 
weight  of  the  lamp  and  the  angle  of  sag  of  the  ropes,  as 
shown  in  figure  117,  we  can  calculate  the  tension  in  the 
ropes. 


Suppose  that  the  weight  of  the  lamp  is  50  pounds,  and  that  the  rope 
ALB  sags  so  as  to  make  both  the  angle  ALR  and  the  angle  BLR  equal 


110 


PRACTICAL  PHYSICS 


to  75°.  In  the  diagram  (Fig.  117)  draw  the  arrow  LW  down  from  L  to 
represent  50  pounds  on  some  convenient  scale.  As  the  two  ropes  have 

to  hold  up  the  lamp,  the  result- 

72  ant  of  the  forces  representing 

the  tension  in  the  ropes  must 
be  equal  and  opposite  to  the 
force  representing  the  weight. 
So  we  draw  LR  equal  and  op- 
posite to  L  W.  Then  we  con- 
struct a  parallelogram  on  LR 
as  a  diagonal  with  its  sides 
FIG.  117.— Three  forces  acting  on  street  lamp,  parallel  to  LA  and  LB,  Ry 

being  drawn   parallel  to  LA, 

and  Rx  parallel  to  LB.  Ly  represents  the  tension  in  the  rope  LB  and 
is  equal  to  about  96.6  pounds,  and  Lx  represents  the  tension  in  LA  and 
is  also  equal  to  about  96.6  pounds. 

Another  good  example  of  the  resolution  of  one  force  into 
two  forces  which  just  balance  it,  is  the  case  of  a  street  lamp 
hung  out  on  a  bracket  from  a  pole,  as  shown  in  figure  118  (a). 


LQSOlb 


1 

W50  Ib. 


Cb} 


FIG.  118.  —  Three  forces  acting  on  lamp  hung  on  bracket. 

Suppose  the  lamp  Z,  weighing  50  pounds,  is  hung  out  from  a  pole  PC 
by  means  of  a  stiff  rod  AB,  10  feet  long,  and  a  tie  rope  or  wire  BC, 
which  is  fastened  to  the  pole  at  C,  3  feet  above  A.  What  is  the  force 
exerted  by  the  rope  BC  ? 

In  the  diagram  (Fig.  118  (6)),  the  weight  of  the  lamp  is  represented  by 
OW,  the  push  of  the  rod  AB  by  OP,  and  the  tension  of  the  tie  rope  BC 
by  OT.  Since  we  know  the  force  OW  (50  pounds),  we  draw  this  line  to 
some  convenient  scale.  The  resultant  of  OP  and  OT  must  be  equal  and 
opposite  to  OW.  Therefore  we  make  OR  equal  and  opposite  to  OW. 


NON-PARALLEL  FORCES  111 

Then,  completing  a  parallelogram  on  OR  as  a  diagonal,  we  have  OP 
representing  the  push  of  the  rod  against  the  lamp,  and  OT  the  tension 
in  the  tie  rope  BC.  If  we  draw  these  lines  carefully  to  scale,  we  find 
that  the  tension  is  174  pounds. 

In  general,  a  single  force  may  be  resolved  into  two  compo- 
nents acting  in  given  directions,  by  constructing  a  parallelogram 
whose  diagonal  represents  the  given  force,  and  whose  sides  have 
the  given  directions  of  the  components. 

112.  Component  of  a  force  in  a  given  direction.  If  a  force 
is  given,  we  can  find  two  other  forces,  one  of  which  repre- 
sents the  whole  effect  in  a  given  direction  of  the  given  force. 

Thus  in  figure  119  we  have  a  canal  boat  AB  which  is  be- 
ing towed  by  the  rope  BO.  We  may  resolve  the  force  along 
the  rope  BO  into  two  components,  one  of  which,  BE,  is 


c 

FIG.  119.  — Useful  component  of  force  on  canal  boat. 

effective  in  pulling  the  boat  along  the  canal,  and  the  other, 
BD,  at  right  angles,  is  useless  or  worse  than  useless,  since  it 
tends  to  pull  the  boat  toward  the  bank.  BE,  the  useful 
component  of  BO,  can  be  computed  by  drawing  the  force 
BO  to  scale  and  then  constructing  a  rectangle  on  BO  as  a 
diagonal,  such  as  BEOD. 

113.  Applications  of  the  principle  of  parallelogram  of  forces. 
This  principle  is  one  of  the  foundation  stones  in  the  study  of 
mechanics.  When  stated  with  the  aid  of  a  geometrical 
diagram,  it  seems  simple,  but  when  met  in  a  crane,  derrick, 
bridge,  or  roof  truss,  it  is  puzzling.  This  is  because,  in 
solving  practical  problems,  we  seldom  find  bodies  which  are 
small  enough  to  be  regarded  as  points  at  which  forces  act. 
Nevertheless  we  can  do  problems  by  this  method,  even  when 
the  bodies  are  quite  large.  For  if  any  body  is  held  still  by 


112 


PRACTICAL  PHYSICS 


three   forces,  their   lines   of  action,  if  prolonged,  must   go 
through  a  single  point,  as  shown  in  figure  120  (a).     If  this 

were  not  true  of 
three  forces  act- 
ing on  a  body 
(Fig.  120  (5)), 
B  it  would  spin 
around.  So  we 
can  think  of  the 
forces  as  acting 


(a) 


FIG.  120.  —  Condition  of  spin  and  rest. 


at  a  single  point,  even  though  the  body  in  which  the  point 
lies  is  quite  large. 

114.  Roof  truss.  When  a  wooden  house  is  built,  the  roof 
is  usually  supported  by  pairs  of  timbers  set  like  an  inverted 
V,  as  in  figure  121.  Each 
pair  of  timbers  has  to 
carry  the  weight  of  a  sec- 
tion of  the  roof,  and,  in 
winter,  of  the  snow  and 
ice  that  accumulate  on  it. 
This  weight  is  really  dis- 
tributed along  the  tim- 


m 

FIG.  121.  — Roof  trusses. 


bers,  but  it  can  be  thought 

of   as   concentrated,   half 

at  the  peak  and  half  at  the  eaves,  where  it  rests  directly  on 

the  walls.     The  part  of  the  load  that  is  at  the  peak  tends  to 

"  spread  "  the  inverted  V,  arid  our  problem  is  to  find  what  has 

to  be  done  to  prevent  this. 

We  may  test  this  experimentally  with  a  small  model  of  a  pair  of  roof 
trusses  (Fig.  122).  These  have  hinges  at  the  top  instead  of  a  stiff  joint, 
and  frictionless  wheels  underneath,  so  that  they  will  not  stand  up  at  all 
under  the  load  W  unless  a  tie  is  put  across  the  bottom  of  the  A  to  pre- 
vent the  spreading.  If  a  spring  balance  is  put  into  the  tie,  the  pull 
which  the  tie  has  to  exert  on  the  truss  members  can  be  measured.  If 
the  load  at  the  peak  is  50  pounds,  and  if  the  truss  members  make  a  right 
angle,  the  "  tension  "  in  the  tie  will  be  about  25  pounds. 


NON-PARALLEL  FORCES  lib 

In  discussing  this  experiment,  we  have  to  apply  the  parallelogram  of 
forces  at  two  points  separately.  In  the  first  place,  let  us  consider  the  pin 
of  the  hinge  at  the  top.  This  is  acted  on  by  three  forces,  the  pull  of  the 
weight  W,  and  the  push  exerted  by  each  rod  (Fig.  122).  Since  these 
balance,  we  can  find  each  push  by  constructing  a  parallelogram  whose 
diagonal  is  equal  and  opposite  to  W.  If  the  rods  are  at  right  angles,  this 
parallelogram  is  a  square,  and  each  push  is  50/V2,  or  35.3  pounds. 


\ 

FIG.  122. —  Experimental  roof  truss,  and  force  diagram. 

Turning  next  to  the  pin  at  the  foot  of  one  rod,  we  see  that  it  is  also 
acted  on  by  three  forces,  the  push  of  the  rod,  35.3  pounds,  the  pull  of  the 
tie  wire,  and  the  push  upward  exerted  by  the  table.  Since  these  balance, 
we  can  get  the  last  two  by  constructing  a  parallelogram  on  the  known 
force  as  a  diagonal  (draw  this  yourself) .  This  parallelogram  is  composed 
of  two  45°  triangles,  and  so  both  the  pull  of  the  tie  wire  and  the  push  of 
the  table  are  35.3/V2,  or  25  pounds. 

In  building  a  roof,  the  pull  exerted  by  the  tie  wire  in  our 
experiment  has  to  be  provided  for  in  some  way.  Usually 
the  ends  of  the  roof  timbers  are  nailed  to  the  frame  of  the 
building,  which  is  stiff  enough  to  exert  a  part  or  all  of  the 
required  force.  Often  a  board  is  nailed  across  the  inverted 
V,  either  at  the  bottom,  or  a  little  higher  up,  to  help  exert  it. 
In  large  roof  trusses,  as  in  churches,  an  iron  rod  is  strung 
across  and  tightened  with  a  screw  coupling. 

115.  Bridge.  Large  bridges  are  built  of  wood  or  steel 
"members"  joined  to  form  a  number  of  adjacent  triangles. 
If  the  members  are  strong  enough  not  to  stretch  or  shrink 


114 


PRACTICAL  PHYSICS 


under  the  loads  imposed  on  them,  each  triangle,  having  three 
sides  of  unchanging  length,  keeps  its  shape,  and  so  the  whole 
truss  is  rigid. 

In  very  large  bridges  the  members  are  joined  together  at 
the  corners  of  the  triangles  by  boring  holes  in  them  and 
thrusting  a  steel  pin  through  all  the  holes  at  a  joint. 
Bridges  made  in  this  way  are  called  pinned  bridges.  The 
plate  opposite  page  114  shows  two  such  bridges.  In  designing 
a  pinned  bridge,  an  engineer  computes  the  "stresses  in  the 
members,"  that  is,  the  forces  which  they  have  to  exert  to 
hold  the  bridge  stiff  under  load,  by  applying  the  parallelo- 
gram of  forces  to  the  pin  at  each  joint  separately.  The 
members  which  have  to  push  against  the  pins  at  their  ends 
are  called  compression  members,  because  they  tend  to  shorten 
under  load,  while  those  that  have  to  pull  on  the  pins  at  their 
ends  are  tension  members,  and  tend  to  lengthen  under  load. 
In  large  bridges  it  is  easy  to  see  which  are  compression 

members  and  which 
tension,  for  the  com- 
pression members  are 
made  broad  and  stiff 
with  "  latticing "  up 
their  sides,  while  the 
tension  members  are 
steel  straps  or  rods 
with  enlarged  ends  to 
give  room  for  the 
holes.  Thus  the  heavy 

FIG.  123.  — Diagrams  of  the  bridges  in  the  plate    r  -,  OQ  •     r 

opposite  page  114  lmes  m  %ure  123  mdl" 

cate  compression  mem- 
bers, while  the  light  lines  correspond  to  tension  members. 

In  smaller  bridges  the  members  are  not  joined  by  pins, 
but  are  riveted  to  "  gusset  plates "  at  each  joint.  Such 
bridges  are  designed  as  if  they  were  pinned,  the  stiff  joints 
giving  an  additional  factor  of  safety. 


Framed  bridges  with  pinned  joints.  The  upper  one  is  a  "  through-bridge  "  with 
9  "panels,"  the  lower  a  "  deck-bridge  "  with  only  5  "panels."  Notice,  how- 
ever, that  the  essential  features  of  the  two  trusses  are  alike. 


NON-PARALLEL  FOECES 


115 


f. 


The  smallest  steel  bridges  are  supported  by  plate  girders, 
one  on  each  side,  which  are  simply  stiff  steel  beams,  and  will 
be  discussed  in  the  next  chapter. 

Roofs  of  large  span  are  often  supported  by  framed  trusses, 
made  of  members  forming  triangles,  like  bridge  trusses. 

116.  How  a  boat  sails  into  the  wind.     Let  AB  (Fig.  124) 
represent  a  boat,  SS'   its  sail,  and   W  the  direction  of  the 
wind.     It  is  sometimes  hard  to  see 

how  such  a  wind  pushes  the  boat 
ahead  instead  of  forcing  it  back- 
ward. The  wind  blowing  it 
against  a  slanting  sail  SS'  is  de- 
flected and  causes  a  pressure  per- 
pendicular to  the  surface.  This 
pressure  can  be  represented  by  the 
arrow  cP  in  the  diagram.  The 
force  cP  can  be  resolved  into  two 
components,  one  useful,  ck,  which 
is  parallel  to  the  keel  of  the  boat, 
and  the  other  useless,  cw,  which  tends  to  move  the  boat  to 
leeward.  This  sideways  movement  is  largely  prevented  by 
a  deep  keel  or  a  centerboard.  So  the  net  effect  of  the  wind 
is  to  drive  the  boat  forward. 

117.  What  supports  an  aeroplane  ?     An   aeroplane  of  the 
monoplane  type  has  one  huge  plane  or  sail,  and  a  biplane  two 
such  planes,  one  above  the  other.     These  planes  are  tilted  so 
that  the  front  edge  is  a  little  higher  than  the  rear  edge. 
There  is  also  a  light  but  powerful  gasolene  engine  which,  by 
turning   one   or  two  large  propellers,  forces  the   aeroplane 
forward.     How  such  a  machine,  which  is  heavier  than  air, 
is  kept  up,  will  be  seen  from  figure  125.     Let  AB  represent 
a  tilted  plane  moving  from  right  to  left.     The   conditions 
are  evidently  the  same  as  if  the  plane  stood  still  and  a  strong 
wind  was  blowing,  as  shown  by  the  arrows.     The  air  strik- 
ing against  the  under  side  of  the  plane  AB  is  deflected  and 


FIG.  124.  —  Action  of  wind  on  a 
sail. 


116 


PRACTICAL  PHYSICS 


causes  a  pressure  OP  at  right  angles  to  the  surface.     It  is  the 
upward  component  of  this  force  which  keeps  the  aeroplane 

from  falling.  The  weight 
of  the  machine,  including 
the  engine  and  load,  is 
represented  by  0  W. 
The  driving  force  of  the 
propeller  OT  must  be 
equal  to  the  resultant  of 
the  two  forces  OP  and 
OW  to  keep  the  machine 

-Direction  *  flight  from  slowing  up. 


FIG.  125.  —  Forces  acting  on  aeroplane. 


118.  Friction  on  an  in- 
clined plane.  When  an 
object  is  placed  on  an  inclined  plane,  friction  tends  to  keep 
the  object  from  sliding  down  the  plane  (Fig.  126).  If  the 
angle  of  inclination 
is  small  enough, 
this  friction  will 
prevent  the  object 
from  sliding  down 
the  plane. 

For   example, 

.    .      •  -  B 

suppose  an  electric 

FIG.  126.  — Friction  on  inclined  plane. 

car  is  on  a  grade 

with  the  brakes  set,  so  that  the  car  stands  still.  How  steep  can 
the  grade  be  before  the  car  slides  down?  In  the  diagram, 
figure  126,  let  0  W  represent  the  weight  of  the  car,  OP  the 
pressure  of  the  inclined  plane  against  the  car,  and  OF  the 
friction  which  retards  its  motion.  When  these  three  forces 
are  in  equilibrium,  the  resultant  of  OP  and  OW,  that  is,  OR, 
must  be  opposed  by  an  equal  force  OF.  Now  OjPcan  never 
exceed  a  limiting  value  which  depends  on  the  pressure  and 
on  the  coefficient  of  friction,  the  latter  being  determined  by  the 
condition  of  the  track.  But  the  resultant  OR  increases  as 


NON-PARALLEL  FORCES  117 

the  incline  becomes  steeper.  So,  as  the  steepness  increases, 
we  soon  reach  a  condition  in  which  OR  is  greater  than  OF 
possibly  can  be,  and  the  car  slides  down.  If  we  know  the 
coefficient  of  friction  between  the  wheels  and  the  rails,  we 
can  compute  the  grade  at  which  the  car  will  begin  to  slide. 

Let  figure  126  represent  this  grade.  We  have  already 
(section  45)  denned  the  coefficient  of  friction  as  the  ratio 
between  friction  and  pressure,  and  so,  in  this  case,  we  have 

Coefficient  of  friction  =         =  777,- 


From  geometry  we  know  that  the  triangles  OPR  and  XTZ 
are  similar  since  they  are  mutually  equiangular.  It  follows 
that 

OR  _H  _  height  of  plane 

OP     B        base  of  plane 

Therefore 


Coefficient  of  friction  =  hei*ht  of          . 
base  of  plane 

This    is    a    convenient    way   of    measuring    coefficients   of 
friction. 


PROBLEMS 

1.  If  the  resultant  of   two  components  acting  at  right  angles  is  50 
pounds,  and  one  of  the  forces  is  15  pounds,  what  is  the  other  force  ? 

2.  One  of  two  components  acting  at  right  angles  is  three  times  the 
other.     Their  resultant  is  32  pounds.     Find  the  forces. 

3.  A  force  of  8  pounds  is  to  be  resolved  into  two  forces,  one  of  which 
is  12  pounds,  and  makes  an  angle  of  90°  with  the  given  force.     Find  the 
other  force. 

4.  A  boy  weighing  50  kilograms  sits  in  a  hammock  whose  ropes  make 
angles  of  30°  and  60°,  respectively,  with  the  vertical.     What  is  the  ten- 
sion in  each  rope  ? 

5.  Each  rope  in  problem  4  is  fastened  to  a  hook  in  the  ceiling.     Find 
the  vertical  pull  on  each  hook. 


118 


PRACTICAL  PHYSICS 


6.  Figure  127  shows  a  simple  crane.     Find  the  tension  in  the  tie  rope 
BC  and  the  push  of  the  brace  AC,  when  the  weight   W  is  one  ton,  and 
the  angle  BA  C  is  45°. 

7.  In  figure  119  the  canal  boat  is  10  feet  from  the  shore,  and  a  pull 
of  200  pounds  is  exerted  on  the  50-foot  towline.     What  is  the  effective 
component? 


000  Us, 


w 


FIG.  127.  —  Diagram  of  simple 
crane. 


FIG.  128.  — Girder  supported 
from  a  wall. 


8.  One  end  of  a  horizontal  steel  girder  10  feet  long  rests  on  a  ledge 
in  the  wall,  and  the  other  end  is  supported  by  a  steel  cable  arranged  as 
shown  in  figure  128.  Assuming  that  the  girder  weighs  40  pounds  per 
foot,  find  the  tension  in  the  cable. 


SUMMARY   OF  PRINCIPLES   IN  CHAPTER  V 
Forces  can  be  represented  by  arrows. 

The  parallelogram  of  forces : — 

The  resultant  of  two  forces  is  the  diagonal  of  their  parallelogram. 
The  equilibrant  of  two  forces  is  equal  and  opposite  to  their 
resultant. 

If  three  forces  act  on  a  body  (not  a  point),  their  lines  of  action 
must  pass  through  a  single  point,  and  the  parallelogram  prin- 
ciple can  be  used. 


NON-PARALLEL  FORCES  119 


QUESTIONS 

1.  Show  by  a  diagram  the  useful  component  of  the  pull  exerted  on 
a  sled  by  a  rope. 

2.  Why  is  a  long  towline  more  effective  in  "hauling  a  canal  boat 
than  a  short  line? 

3.  Why  does  one  lower  the  handle  in  pushing  a  lawn  mower  through 
tall  grass  ? 

4.  A  boat  is  rowed  across  a  river.     What  two  forces  are  acting  on 
the  boat? 

5.  A  child  sitting  in  a  swing  is  drawn  gradually  aside  by  a  force 
which  continually  acts  in  a  horizontal  direction.     Does  the  tension  in 
the  swing  rope  grow  smaller  or  larger? 

6.  Why  will  a  long  rope  hanging  between  two  points  at  the  same 
level  break  before  it  can  be  pulled  tight  enough  to  be  straight  ? 

7.  Find  in  some  building  a  roof  truss  with  a  steel  tie  rod  to  keep  it 
from  spreading. 

8.  How  are  the  walls  of  Gothic  cathedrals  strengthened  so  that  they 
can  exert  the  side  thrust  necessary  to  hold  up  the  roof? 

9.  Examine  the  steel  bridges  in  your  neighborhood  to  see  if  they  are 
"  girder  bridges  "  or  "  framed  bridges,"  and,  if  any  of  them  are  framed, 
see  whether  they  are  pinned  or  riveted,  and  which  members  are  com- 
pression members,  and  which  tension.     Make  a  sketch  like  those  in 
figure  123  of  one  of  these  bridges,  showing  the  compression  members  by 
heavy  lines. 

10.  Explain  by  diagram  how  an  ice  boat  may  go  faster  than  the  wind. 

11.  Could  an  ordinary  balloon  "  tack  "  against  the  wind  like  a  sail- 
boat, if  it  was  provided  with  a  sail,  a  large  keel,  and  a  rudder,  like  a 
sailboat?     Why? 


CHAPTER  VI 
ELASTICITY  AND    STRENGTH   OF    MATERIALS 

The  different  kinds  of  stress  —  stress  and  strain  —  Hooke's 
law  —  elastic  limit  —  breaking  strength  —  factor  of  safety. 

Unit  stress  and  unit  strain  in  tension  —  tensile  strength  — 
stiffness  and  strength  of  beams  —  cross  sections  of  beams. 

119.  Importance    of    studying    materials.       A   structural 
engineer  who  is   to  build  a  bridge,   a  building,  or  a  ma- 
chine must  know  not  only  the  forces   that  will  be  exerted 
on  each  of  its  parts,  but  also  the  strength  of  the  wood,  brick, 
stone,  or  steel  of  which  they  are  to  be  made.     This  knowledge 
can  be  gained  only  by  testing  each  kind  of  material  with 
the  greatest  care.     For  this  reason,  every  engineering  hand- 
book tabulates  the  results  of  a  great  number  of  tests  of  this 
kind.     Every  large  manufacturer  of  steel  girders  or  rails 
maintains  a  testing  laboratory  so  that  he  can  sell  his  prod- 
ucts under  a  strength  guarantee.     Even  textile  manufac- 
turers test  the  breaking  strength  of  the  yarn  that  goes  into 
their  cloth.     Indeed,  the  study  of  the  properties  of  struc- 
tural materials  is  regarded  as  of   such   importance   to  the 
public  that  the  government  itself  maintains  a  bureau  for  the 
purpose.     In  this  chapter  we  shall  learn  how  to  make  such 
tests  on  a  small  scale,  and  how  the  results  are  used. 

120.  The    different   kinds   of    stresses.       In   designing    a 
beam  or  column,  or  some  part  of  a  machine,  an  engineer  must 
first  know  how  the  force  it  is  to  resist  will  be  applied. 

For  instance,  the  cable  that  supports  an  elevator,  or  the 
rope  of  a  swing,  or  a  belt  that  is  transmitting  power  from 
one  pulley  to  another,  has  to  resist  a  pull  applied  at  each 

120 


ELASTICITY  AND   STRENGTH  OF  MATERIALS        121 


end,  which  tends  to  stretch  it,  and  may,  perhaps,  break 
it  by  pulling  one  part  of  it  away  from  the  next.  In  such 
a  case  we  say  that  the  "member  "  —  that  is,  the  cable,  or  rope, 
or  belt  —  is  in  tension,  meaning  "in  a  state  of  tension." 

The  pier  of  a  bridge,  or  the  foundation  of  a  house,  or  a 
post  supporting  a  piazza  roof,  has  to  do  something  quite 
different  from  this.  It  has  to  resist  a  push  at  each  end, 
which  tends  to  shorten  it,  and  may  cause  it  to  give  way  by 
crushing  it.  In  such  a  case  we  say  that  the  member  —  that 
is,  the  pier,  or  foundation,  or  post — is  in  compression,  meaning 
"in  a  state  of  compression." 

A  floor  beam  in  a  house  or  a  girder  in  a  plate-girder 
bridge  (section  115)  has  to  resist  bending,  and  if  it  gives 
way  at  all,  it  does  so  by  breaking  in  two  like  a  stick  broken 
across  one's  knee. 

The  duty  of  the  shaft  that  drives  the  propeller  of  a  steam- 
ship, or  of  the  shafts  that  run  overhead  in  many  factories 
and  transmit  power  to  the  various  machines,  is  to  resist 
twisting. 

And,  finally,  the  duty  of  a  rivet  in  a  steel  structure  is 
different  from  any  of  these  (see  Fig.  129).  It  has  to  keep 
one  of  the  plates  from  sliding  over 
the  other.  When  such  a  rivet  gives 
way,  it  is  often  because  the  halves 
of  it  have  been  pushed  sidewise 
so  hard  that  one  has  slid  away 
from  the  other,  leaving  a  flat,  clean 
break  parallel  to  the  surface  sepa- 
rating the  plates.  It  is  a  strain  of  FIG.  129.  —  Action  of  plates  on 
this  sort  that  we  are  really  putting  nvet* 

on  a  piece  of  cloth  or  paper  when  we  cut  it  with  a  pair  of 
shears.  So  we  say  that  the  rivet  is  in  shear,  meaning  that 
it  is  in  the  same  state  as  if  it  were  being  cut  in  two  by  a 
pair  of  huge  shears. 

There  are,  then,  these   five   kinds   of   stresses:    tension, 


122 


PEACTICAL  PHYSICS 


compression,  bending,  twisting,  and  shear.  In  each  case 
that  material  should  be  used  which  will  best  resist  the 
particular  kind  of  stress  that  is  to  be  applied  to  it.  Thus 
bricks  set  in  mortar  do  very  well  under  compression,  but 
are  of  little  use  in  resisting  any  of  the  other  kinds  of  stress. 
Steel  will  resist  any  of  them  well.  Cast  iron  will  resist 
compression  about  four  times  as  well  as  it  will  tension,  and 
so  on. 

121.  Stress  and  strain.  Whenever  any  one  of  these 
kinds  of  stress  is  applied  to  a  body,  the  body  yields  a  little. 
No  bridge  girder  is  stiff  enough  not  to  bend  a  little  under 
every  wagon  or  train  that  goes  over  the  bridge.  If  it  is 
a  good  girder,  the  amount  of  bending  is  imperceptible  to 
ordinary  observation  ;  but  there  is  always  some  bending. 
Similarly,  every  shaft  on  a  steamship  twists  a  little 
when  the  propeller  is  in  motion.  Measuring  this 
very  small  twist  is  often  the  only  way  in  which  the 
horse  power  delivered  by  the  engine  to  the  propeller 
can  be  measured.  The  same  can  be  said  of  the 
other  types  of  stress  ;  each  of  them  always  causes 
some  yielding  or  deformation  of  the  body  under 
stress. 

The  word  "  strain  "  is  used  to  describe  the 
deformation  produced.  The  word  stress  always 
refers  to  the  forces  which  are  acting,  while  the 

word  strain  refers  to 
the  effect  which  they 
produce. 

122.    Relation  of 
strain  to  stress.     Let 


FIG.  130.  -Stretching  a  wire  with    us     tr7    some 

different  loads.  ments  to  see  if  there 

is  any  relation  between 
the  amount  of  stress  applied  to  a  body  and  the  amount 
of  strain  it  produces. 


ELASTICITY  AND   STRENGTH  OF  MATERIALS        123 


I.  Tension.     Let  us  fasten  one  end  of  a  piece  of  steel  or  spring-brass 
wire  in  a  clamp  near  the  ceiling,  and  attach  a  pan  for  weights  to  the 
lower  end  of  the  wire  (Fig.  130).     Since  the  stretch  will  be  small,  it  is 
necessary  to  use  a  lever  or  some  other  device  to  magnify  it.     Having 
placed  just  enough  weight  in  the  pan  to  straighten  the  wire,  we  add 
weights  one  at  a  time  and  read  the  corresponding  positions  of  the  pointer. 
Each  time  we  must  remove  the  added  weights  to  see  if  the  pointer  comes 
back  to  its  original  position.     When  it  fails  to  do  this,  we  will  stop 
the  experiment  and  disregard,  for  the  moment,  the  last  reading  of  the 
pointer.     If  we  then  compute  from  each  deflection  of  the  pointer  the 
actual  stretch  or  elongation   of  the  wire,  and  divide  each  stretch  by 
the  force  causing  it,  we  will  find  that 

all  the  quotients  are  approximately 
the  same.  That  is,  the  stretch  is 
proportional  to  the  load. 

II.  Compression.      The    same    is 
true  for  compression.     Thus  experi- 
ments have  shown  that  under  ordi- 
nary conditions  the  compression  of 
a  spring  is  proportional  to  the  force 
applied. 

III.  Bending.     We  can  perform  a 
similar  experiment  for  bending  by 
supporting  a  metal  rod  or  tube  on 
knife  edges,   and  hanging  different 
weights  from  the  center.     A  lever, 
like  that  used  in  the  tension  experi- 
ment above,  enables  us  to  measure 
the  small  deflections  of  the  center  of 


FIG.  131.— Twisting  metal  rods. 


the  rod.     As  before,  we  find  that  the  deflections  are  proportional  to  the 
loads  causing  them. 

IV.  Twisting.  The  apparatus  shown  in  figure  131  enables  us  to  per- 
form similar  experiments  on  twisting.  As  before,  we  find  that  the  twist 
is  proportional  to  the  stress  causing  it,  namely,  the  "  torque  "  or  moment 
of  the  twisting  force. 

In  all  these  cases,  the  strain  is  proportional  to  the  stress. 
This  is  called  Hooke's  law,  after  the  medieval  scientist  who 
discovered  it.  Hooke's  law  applies  to  all  kinds  of  strains, 
if  the  stresses  are  not  too  great. 


124  PRACTICAL  PHYSICS 

PROBLEMS 

1.  If  a  weight  of  1  pound,  when  hung  on  a  certain  spring,  lengthens  it 
2  inches,  what  weight  would  lengthen  it  \  an  inch?     How  much  would  f 
of  a  pound  lengthen  it? 

2.  If  a  force  of  5  pounds  is  required  to  move  the  middle  point  of  a 
beam  ^  of  an  inch,  what  force  would  move  it  £  an  inch? 

3.  A  2  pound  force  is  applied  to  the  rim  of  a  wheel  9  inches  in  diam- 
eter in  the  torsion  apparatus  described  in  section  122,  and  the  end  of 
the  rod  twists  through  3°.     What  force  would  have  to  be  applied  to  the 
rim  of  a  wheel  12  inches  in  diameter  to  make  the  end  of  the  same  rod 
twist  through  5°? 

123.  Elastic  limit  and  breaking  strength.  In  the  tension 
experiment  in  the  last  section  we  found  that  when  a  suffi- 
ciently great  load  was  hung  from  the  wire,  the  latter  did  not 
shrink  back  to  its  original  length  when  the  load  was  removed. 
It  had  acquired  a  permanent  "  set."  The  same  thing  is  true 
of  other  kinds  of  stress,  and  might  have  been  noticed  in  the 
other  experiments.  The  smallest  stress  of  any  particular 
kind  that  will  cause  a  permanent  set  in  a  body  is  called  the 
elastic  limit  of  the  body  for  that  particular  kind  of  stress. 
As  long  as  the  load  is  below  the  elastic  limit,  Hooke's  law 
holds,  but  stresses  greater  than  the  elastic  limit  cause  deflec- 
tions greater  than  Hooke's  law  predicts. 

If  we  still  further  increase  the  load  in  the  tension  ex- 
periment, we  finally  reach  a  load  so  great  that  the  wire 
stretches  very  rapidly  and  almost  immediately  breaks. 
This  is  also  true  of  other  kinds  of  tests,  such  as  tests  for 
bending.  The  smallest  stress  of  any  particular  kind  that 
will  cause  a  body  to  give  way  is  called  the  ultimate  or 
breaking  strength  of  the  body  for  that  particular  kind  of  stress. 

Usually  the  elastic  limit  of  anything  is  much  smaller  than 
its  breaking  strength.  But  certain  materials,  such  as  glass, 
follow  Hooke's  law  right  up  to  their  breaking  points,  and 
never  show  a  permanent  set.  In  such  cases,  the  elastic  limit 
and  the  breaking  strength  are  equal. 


ELASTICITY  AND   STRENGTH  OF  MATERIALS        125 

124.  Factor   of  safety.     An  engineer,  when  designing   a 
bridge  or  a  machine,  must  be  absolutely  sure  that  no  part  of 
it  will  ever  be  subjected  to  a  stress  greater  than  its  elastic 
limit,  for  if  this  were  to  happen,  the  part  would  be  perma- 
nently deformed,  and  this  would  weaken   the   rest   of   the 
structure,  or  at  least  throw  it  out  of  alignment.     He  there- 
fore plans  to  make  each  member  big  enough  to  carry  several 
times  as  much  load  as  will  probably  ever  be  imposed  on  it. 
This  is  partly  to  provide  for  any  unforeseen  temporary  over- 
loading of  the  structure,  and  partly  because  there  may  be, 
even  in  materials  of   the  best  quality,  imperceptible    flaws 
that  would  make  the  completed  member  less  strong  than  it 
seems  to  be.     The  number  of  times  that  the  load  planned 
for  is  greater  than  the  load  expected  is  called  the  factor  of 
safety. 

The  factor  that  should  be  used  varies  with  the  material; 
thus  it  is  commonly  10  for  brick  and  stone  and  only  4  for 
steel.  It  also  varies  with  the  nature  of  the  load;  thus  it  is 
commonly  larger  when  the  load  is  to  be  intermittent,  as  in 
machines  or  railroad  bridges,  than  when  it  is  to  be  steady, 
as  in  buildings.  Often  the  factor  for  buildings  is  taken 
larger  than  would  otherwise  be  necessary,  so  that  there  may 
be  no  danger  of  deflections  in  the  walls  and  ceilings  great 
enough  to  crack  the  plaster. 

125.  Unit  stress  and  unit  strain  in   tension.      When   we 
discussed  Hooke's  law  in  section  122,  we  were  comparing 
with  each  other  the  deformations  produced  in  the  same  wire 
or  rod  by  forces  of  different  magnitudes.     That  is,  if   we 
knew  by  experiment  how  much  one  force  would  stretch  a 
given  wire,  we  could  compute  how  much  a  different  force 
would  stretch  the  same  wire.     Let  us  now  see  if  we  can  com- 
pute from  the  result  of  an  experiment  on  one  wire  how  much 
another  wire  of  the  same  material  but  of  a  different  shape 
would  be  stretched  by  any  force  that  might  be  applied  to  it. 
This  is  important  for  the  engineer  because  it  enables  him  to 


126  PRACTICAL   PHYSICS 

test  a  small  piece  of  a  particular  kind  of  steel,  and  compute 
from  this  how  a  large  tension  bar  in  a  bridge  will  act.  For 
this  purpose  it  will  be  convenient  to  define  more  precisely 
than  in  section  121  the  meaning  of  "  stress  "  and  "  strain  "  in 
the  case  of  a  wire  or  rod  under  tension. 

If  one  wire  is  twice  as  long  as  another,  a  given  pull  will 
stretch  the  long  wire  twice  as  much  as  the  short  one ;  for 
each  half  of  the  long  wire  is  just  like  the  whole  of  the  short 
one,  and  has  to  pull  just  as  hard  on  its  supports ;  each  half, 
then,  stretches  as  much  as  the  whole  of  the  short  wire.  In 
general,  the  total  stretch  of  a  wire  under  a  given  load  is  pro- 
portional to  its  length.  The  stretch  per  unit  of  length  is  called 
the  unit  stretch  or  unit  strain. 

Unit  stretch  =  total  stretch , 
length 

For  example,  a  piece  of  steel  piano  wire,  originally  90  inches  long,  is 
stretched  0.033  inches  by  a  certain  load.  Then  the  unit  stretch  or  unit 
strain  is  0.033/90  or  0.00037  inches  per  inch  of  length. 

Similarly  if  two  wires  are  of  the  same  length,  but  one  has 
twice  as  great  an  area  of  cross  section  as  the  other,  the  thick 
wire  is  equivalent  to  two  of  the  thin  wires  side  by  side,  and 
it  would  take  twice  as  much  force  to  stretch  the  thick  wire  a 
given  amount  as  to  stretch  the  thin  wire  the  same  amount. 
In  general,  the  pull  required  to  produce  a  given  stretch  will 
be  proportional  to  the  area  of  cross  section.  The  pull  per 
unit  area  of  cross  section  is  called  the  unit  pull  or  unit  stress. 

Unit  pull  =  -      total  pun 

area  of  cross  section 

For  example,  a  piece  of  steel  piano  wire  0.0348  inches  in  diameter  is 
subjected  to  a  pull  of  10  pounds.  What  is  the  unit  pull  or  unit  stress  in 
the  wire  ?  The  area  of  the  cross  section  of  the  wire  is  Ttr2  or  3.14  x  0.01 742 
or  0.000950  square  inches.  Therefore  the  unit  stress  is  10/0.000950  or 
10,500  pounds  per  square  inch. 

If  we  were  to  test  with  the  apparatus  described  in  section 
122  a  number  of  wires  of  the  same  material  but  of  different 


ELASTICITY  AND   STRENGTH   OF  MATERIALS        127 

sizes  and  lengths,  we  would  find  that  in  all  cases  the  unit 
stretch  is  proportional  to  the  unit  putt.  This  law  enables  us  to 
compute  how  much  a  force  will  stretch  a  wire,  if  we  know 
how  much  another  force  will  stretch  another  wire  of  the  same 
material. 

For  example,  if  a  10-kilogram  weight  produces  in  a  piece  of  piano 
wire,  0.5  millimeters  in  diameter  and  1  meter  long,  a  stretch  of  0.02  mil- 
limeters, what  will  be  the  stretch  produced  in  a  piece  of  piano  wire  0.4 
millimeters  in  diameter  and  2  meters  long,  by  a  15-kilogram  weight  ? 

For  the  first  wire  :  — 

The  cross  section  is  irr2  =  —  square  millimeters. 
16 

1  f\f\ 

The  unit  pull  is  10  -4-  —  = kilograms  per  square  millimeter. 

16        TT 

The  unit  stretch  is  0.02  millimeters  per  meter. 
For  the  second  wire  :  — 

The  cross  section  is  irr'2  =  —  square  millimeters. 
25 

The  unit  pull  is  15  H-  -^-  =  — —  kilograms  per  square  millimeter. 

2o  7T 

Call  the  unit  stretch  x  millimeters  per  meter. 
Then,  since  the  unit  pulls  and  unit  stretches  are  in  proportion, 

375 


0.02     160 

7T 

or  x  =  0.02  x  —  =  0.047  millimeters  per  meter. 

160 

Since  the  second  wire  is  2  meters  long,  the  total  stretch  in  it  is 
2  x  0.047  =  0.094  millimeters. 

126.  Tensile  strength.  The  length  of  a  wire  or  rod  has 
nothing  to  do  with  its  strength  under  tension,  unless  the  rod 
is  so  long  that  its  own  weight  has  to  be  taken  into  account. 
The  strength  of  a  wire  or  rod  is  proportional  to  the  area  of 
its  cross  section.  The  strength  of  a  wire  or  rod  of  unit  cross 
section  (1  square  inch  or  1  square  centimeter)  is  called  the 


128  PRACTICAL  PHYSICS 

tensile  strength  of  the  material.  Tables  giving  the  breaking 
strengths  of  various  materials  can  be  found  in  any  engineer's 
handbook. 

For  example,  in  a  testing  laboratory  it  was  found  that  a  wrought-iron 
bar  0.75  inches  in  diameter  broke  under  a  pull  of  28,700  pounds.     The 
tensile  strength  of  the  material  was,  then, 
98700 


3.14  x  (0375)2 

PROBLEMS 

1.  If  a  pull  of  22  pounds  will  break  iron  wire  of  size  24,  what  pull 
will  break  iron  wire  of  size  30  ?     (See  table  on  page  304  for  diameters.) 

2.  From  the  data  given  in  problem  1,  compute  the  tensile  strength  of 
the  iron. 

3.  An  iron  bar  is  to  be  subjected  to  a  total  pull  of  35.000  pounds  and 
is  to  be  designed  so  that  the  unit  pull  shall  not  exceed  2500  pounds  per 
square  inch.     What  should  be  the  area  of  its  cross  section,  and  if  round, 
what  should  be  its  diameter  ? 

4.  A  force  of  2  kilograms  stretches  a  certain  wire  3  millimeters.    How 
much  will  a  force  of  5  kilograms  stretch  the  same  wire? 

5.  How  much  would  5  kilograms  stretch  a  piece  of  the  same  kind  of 
wire  as  in  problem  4,  with  the  same  diameter  but  twice  as  long? 

6.  How  much  would  5  kilograms  stretch  a  piece  of  the  same  kind  of 
wire  as  in  problem  4,  of  the  same  length  but  with  twice  the  diameter  ? 

7.  How  much  would  5  kilograms  stretch  a  piece  of  the  same  kind  of 
wire  as  in  problem  4,  but  with  half  the  diameter  and  three  times  the  length  ? 

127.  Stiffness  and  strength  of  beams.  The  design  of  fto«r 
beams  for  buildings  or  girders  for  bridges  is  another  matter 
in  which  it  is  important  for  engineers  to  be  able  to  predict 
from  experiments  on  small  test  pieces  how  a  full-sized  mem- 
be»  will  act.  They  have,  therefore,  tried  many  experiments 
on  beams  of  different  sizes  and  shapes  with  large  test  ma- 
chines similar  in  principle  to  the  bending  apparatus  described 
in  section  122.  These  experiments  have  shown  *#iat  what 
may  be  called  the  stiffness  factor  of  a  beam  of  rectangular 
cross  section  is 

Stiif  ness  factor  =  breadth  x  (depth)*  , 
(length)3 


ELASTICITY  AND   STRENGTH  OF  MATERIALS       129 

To  compare  the  deflections  that  would  be  produced  by  a 
given  force  in  two  beams,  we  have  only  to  compute  their 
stiffness  factors,  and  the  one  with  the  larger  stiffness  factor 
will  bend  less  under  the  given  load. 

For  example,  which  of  the  following  beams  is  stiff er:  — 

Beam  A  :  length  10  feet,  breadth  4  inches,  depth  6  inches ; 
Beam  B :  length  20  feet,  breadth  6  inches,  depth  8  inches? 

Stiffness  factor  of  A  =  4  x  6*  -.  10*  =  9  (b    cancellation). 
Stiffness  factor  of  £      6  x  88  +  208      4  v 

Therefore,  beam  A  is  more  than  twice  as  stiff  as  beam  B;  that  is,  if 
equal  weights  were  hung  from  the  centers  of  the  two  beams,  the  center 
of  A  would  drop  less  than  half  as  far  as  would  the  center  of  B. 

Experiments  have  shown,  however,  that  the  stiffer  of  two 
beams  is  not  necessarily  the  stronger.  In  fact,  the  strength 
factor  of  a  beam  of  rectangular  cross  section  is  quite  different 
from  its  stiffness  factor.  It  is 

Strength  factor  =  breadth  x  (depth)* . 
length 

For  example,  compare  the  strengths  of  the  two  beams  described  above. 

Strength  factor  of  A  ^4  x  &2 -^  10  _  3. 
Strength  factor  of  B  ~  6  x  82  -r-  20      4 ' 

Therefore,  although  beam  A  is  more  than  twice  as  stiff  as  beam  B,  it 
could  support  only  three  quarters  as  much  load  without  breaking. 

128.  Cross  sections  of  beams.  Wooden  beams  ordinarily 
have  a  rectangular  cross  section,  and  are  designed  on  the 
basis  of  the  laws  in  the  last  section ;  but  steel  beanis,  if  so 
designed,  would  be  too  heavy.  It  is  possible,  however,  to 
distribute  a  much  smaller  amount, of  material  in  such  a  way 
as  to  be  just  as  effective.  Thus  we  a^FlTnow  that  a  bicycle 
frame  made  of  thin  tubing  is  mucli^  suffer  than  a  frame  of 
equal  weight  made  of  solid  rods.  So  it  pays  to  consider 
what  the  different  parts  of  the  cross  section  of  a  beam  have 
to  do  to  resist  bending. 


130 


PRACTICAL   PHYSICS 


To  test  this  experimentally  we  have  only  to  bend  a  type* 
writer  eraser  with  our  fingers.  The  result  will  be  as  shown 
in  figure  132.  We  find  that  the  top  layer  of  a  beam  is  short- 


FIG.  132.  —  Diagram  of  loaded  beam. 

ened,  and  has  to  resist  compression,  while  the  bottom  layer  is 
lengthened,  and  has  to  resist  tension.  Somewhere  between 
the  top  and  the  bottom  is  a  layer  mn,  which  remains  of  the 
same  length,  and  does  nothing ;  this  is 
called  the  neutral  layer.  Evidently  there 
should  be  as  much  material  as  possible 
in  the  top  and  bottom  layers,  and  as 
little  as  possible  in  and  near  the  neu- 
tral layer.  This  is  the  case  in  the 
sections  shown  in  figure  133.  It  will 
be  noticed  that  the  material  is  collected 
in  large  flanges  at  the  top  and  bottom,  which  are  joined  by 
one  or  more  thin  webs. 


FlG' 


°f 


PROBLEMS 

1.  A  plank  sags  0.1  inches  with  a  load  of  100  pounds.     How  far  would 
it  sag  under  a  load  of  1  ton  ? 

2.  How  much  would  a  plank  similar  to  that  in  problem  1,  but  twice 
as  wide,  sag  under  a  load  of  1  ton  ? 

3.  How  much  would  a  plank  similar  to  that  in  problem  1,  but  twice 
as  thick  (or  deep),  sag  under  a  load  of  1  ton? 

4.  A  beam  4  inches  wide  and  2  inches  thick,  when  standing  on  edge, 
bends  0.1  inches  per  thousand  pounds.    How  much  per  thousand  would  it 
bend  when  laid  flat  side  down  ? 


ELASTICITY  AND   STRENGTH  OF  MATERIALS       131 

5.   A  modern  floor  beam,  2x9  inches  in  cros*s  section,  contains  only 
half  as  much  material  as  an  old-fashioned  one  6x6.      Compare  the 
modern  beam,  set  on  edge,  with  the  old-fashioned  one,  as  to  both  stiff-    t 
ness  and  strength.  ^  J 

SUMMARY   OF   PRINCIPLES   IN   CHAPTER  VI 

Stress  refers  to  force  acting. 
Strain  refers  to  deformation  produced.    • 
Hooke's  law :   Strain  is  proportional  to  stress*- 
True  for  all  kinds  of  stress. 

.     x    .  ,       total  stretch 
Unit  stretch  =  -  — . 

length 

total  pull 
Unit  pull  = 


area  of  cross  section 
In  tension,  unit  stretch  is  proportional  to  unit  pull,  for  pieces  of 
any  size  or  length,  if  of  same  material. 

In  bending  beams  of  rectangular  cross  section, 

Stiffness  factor  Breadth  x  (depth)* . 
(length)3 

Strength  factor  =  breadth  x  (depth^ 
length 

QUESTIONS 

1.  Why  was  the  standard  meter  bar  (Fig.  1,  section  7)  made  with  a 
nearly  H-shaped  cross  section  ?    Why  was  the  scale  engraved  on  the  hori- 
zontal web  rather  than  on  top  of  one  of  the  sides  ? 

2.  Name  five  practical    applications   of  the  elasticity  of    steel    in 
springs. 

3.  Arrange  an  apparatus  to  determine  whether  or  not   Hooke's  law 
applies  to  a  rubber  band. 

4.  Name  the  kind  of  stresses  which  are   acting  on  the  following: 
wires  of  a  piano,   crank    shalt  in  engine,  smokestack,  table  leg,   belt, 
pump  piston,  and  threads  holding  buttons  on  a  coat. 

5.  In  the  loading  of  long  columns,  what  other  effects  besides  simple 
compression  have  to  be  considered  ? 


132  PRACTICAL  PHYSICS 

6.  Where  is  the  elastic  medium  in  the  human  body  which  prevents 
injury  to  the  brain  when  we  jump? 

7.  In  the  frame  of  a  bicycle,  why  does  a  pound  of  steel  give  greater 
stiffness  in  the  form  of  tubing  than  in  rods  ? 

8.  Which  flange  of  a  cast-iron   girder   should  have  a  greater  cross 
section?     Notice  the  statement  in  section  120. 

9.  Try  to  find  out  what  is  meant>bythe  "fatigue"  of  metals  (see 
encyclopedia). 

10.  What  advantages  has  reenforced  concrete  over  ordinary  concrete 
for  building  purposes? 

11.  How  are  the  walls  of  high  office  buildings  supported,  and  why  V 


,    ,  CHAPTER   VII 

ACCELERATED   MOTION 

Speed  and  acceleration  —  laws  of  motion  at  constant  accel- 
eration —  falling  is  motion  at  constant  acceleration  —  value  of 
acceleration  of  gravity. 

129.  Average  speed.  If  a  man  walks  12  miles  in  3  hours, 
we  say  that  he  averages  4  miles  an  hour.  To  be  sure,  at  any 
particular  point  on  his  journey  he  may  have  been  going 
faster  or  slower,  but  his  average  speed  or  velocity  is  4  miles 
an  hour.  If  we  know  that  the  average  speed  of  a  steamer  is 
22  miles  an  hour,  we  can  find  a  day's  run  by  multiplying 
the  average  speed  by  the  number  of  hours  in  a  day;  thus 
22  x  24  =  528  miles.  In  general, 

Distance  =  average  speed  x  time. 

Speed  is  expressed  in  various  ways;  for  example,  we  say 
that  an  automobile  travels  at  the  rate  of  25  miles  an  hour,  a 
steamer  does  18  knots  or  18  nautical  miles  an  hour,  a  sprinter 
runs  100  yards  in  10  seconds,  and  a  rifle  ball  goes  2000  feet 
per  second.  For  purposes  of  comparison  it  is  convenient  to 
have  some  uniform  way  of  expressing  speed,  and  so  engineers 
and  other  scientific  men  have  come  to  use  feet  per  second 
(ft. /sec.)  or  centimeters  (or  meters)  per  second  (cm. /sec.  or 
m./sec.).  The  following  table  gives  some  average  speeds:  — 

TABLE  OF  SPEEDS 

Soldiers  marching                           4.3  ft./sec.  =  1.4  m./sec. 

Horse  galloping                             16     ft./sec.  =  5.2  m./sec. 

Ocean  steamer                               40     ft./sec.  =  12.2  m./sec. 

Express  train                                 82     ft./sec.  =  26.9  m./sec. 

Wind  in  hurricane                      165     ft./sec.  =  54.2  m./sec. 

Sound                                         1120     ft./sec.  =  386     m./sec. 
Rifle  hall                       1500  to  2000     ft./sec.  =  493  to  657     m./sec. 

133 


134  PRACTICAL   PHYSICS 

QUESTIONS  AND  PROBLEMS 

1.  Sixty  miles  an  hour  equals  how  many  feet  per  second  ?    You  would 
do  well  to  remember  this  number. 

2.  With  the  help  of  a  time-table,  compute  the  average  speed  of  an 
express  train,  and  of  a  local. 

3.  If  the  distance  across  the  Atlantic  Ocean  is  about  3000  miles,  how 
many  days  will  it  take  a  steamer  to  cross,  at  the  speed  given  in  the  table 
above  ? 

4.  An  officer  on  horseback  starts  on  the  gallop  to  overtake  his  regiment 
a  mile  away,  which  is  marching  ahead.     If  they  travel  at  the  speeds  given 
in  the  table,  how  long  will  it  take  him? 

5.  How  long  will  it  take  an  express  train  to  cover  50  miles,  going  at  the 
rate  given  in  the  table  ? 

6.  A  rifle  is  fired  at  a  target  half  a  mile  away.     How  long  after  it  is 
fired  does  the  sound  it  makes  against  the  target  reach  the  man  with  the 
rifle? 

7.  There  is  a  common  rule  that  if  any  one  in  a  train  counts  for  19 
seconds  the  number  of  .clicks  as  the  car  passes  over  the  ends  of  the  rails, 
the  number  he  gets  will  be  the  speed  of  the  train  in  miles  per  hour.     What 
must  be  the  length  of  the  rails  to  make  this  rule  work  ? 

130.  Variable  speed.  When  a  train  is  starting  out  from 
a  station,  it  is  gaining  speed,  and  when  it  is  approaching  a 
station  where  it  must  stop,  it  is  losing  speed.  So  we  see 
that  on  account  of  stops  and  differences  in  grade,  the  speed 
of  a  train  is  not  uniform  or  constant,  but  is  changing  or 
variable.  When  a  loaded  sled  starts  at  the  top  of  a  long  hill, 
it  gains  in  speed  as  it  descends  the  hill ;  but  when  it  reaches 
the  bottom,  it  is  retarded  and  loses  speed  until  it  stops.  Its 
speed  or  velocity,  starting  at  zero,  has  increased  to  a  maxi- 
mum and  then  has  decreased  to  zero  again.  Similarly,  the 
speed  of  a  projectile  from  a  big  gun  or  of  the  piston  of  an  en- 
gine is  not  uniform  but  variable. 

If  we  wished  to  determine  the  speed  of  an  automobile  at 
any  instant  or  point,  we  would  measure  off  some  convenient 
distance  near  the  point  and  then  get  the  time  which  elapsed 
while  the  automobile  traveled  the  fixed  distance.  For  ex- 
ample, if  the  measured  distance,  sometimes  called  a  "  trap," 


ACCELERATED  MOTION  135 

was  a  quarter  of  a  mile  and  the  time  was  20  seconds,  the 
speed  was  three  quarters  of  a  mile  per  minute  or  45  miles 
per  hour,  But  if  the  driver  of  the  automobile  was  aware 
of  the  trap  and  was  driving  at  a  dangerously  high  speed  at 
the  beginning  of  the  trap,  he  would  slow  down  so  that  his 
average  speed  over  the  measured  distance  would  be  within  the 
limit.  To  catch  such  a  driver,  that  is,  to  get  his  speed  more 
accurately  at  any  point,  we  take  as  short  a  distance  as  is 
consistent  with  an  accurate  measurement  of  the  time. 

131.  Acceleration.  It  is  unpleasant  to  be  on  a  street  car 
when  it  starts  or  stops  too  suddenly.  This  suggests  the 
problem  of  measuring  a  rate  of  change  of  speed,  which  is  called 
acceleration.  It  has  been  found  that  a  city  street  car  standing 
at  rest  can  safely  gain  speed,  so  that  at  the  end  of  10  seconds 
it  is  going  15  miles  per  hour.  Assuming  that  this  gain  in 
speed  is  made  at  a  constant  rate  (only  constant  accelerations 
will  be  discussed  in  this  book),  the  speed  of  the  car  increased 
1.5  miles-per-hour  every  second.  In  other  words,  the  accel- 
eration was  1.5  miles-per-hour  per  second.  Or,  since  15 
miles  an  hour  is  22  feet  per  second,  we  can  say  that  the  gain 
in  speed  each  second  is  2.2  feet  per  second. 

In  general, 

Acceleration  =  gain  in  speed  per  unit  time, 

and  acceleration  is  always  to  be  expressed  as  so  many  speed 
units  per  time  unit.  Since  there  are  many  different  speed 
units,  such  as  miles-per-hour,  kilometers-per-hour,  feet-per- 
second,  and  centimeters-per-second,  there  are  many  ways  of 
expressing  the  same  acceleration.  Thus  the  acceleration  of 
the  electric  car  just  mentioned  is 

VELOCITY  UNIT  TIME  UNIT 

1.5  miles-per-hour  per  second, 

or    2.4  kilometers-per-hour        per  second, 

or    2.2  feet-per-second  per  second, 

or  67.0  centimeters-per-second  per  second. 


136  PRACTICAL  PHYSICS 

All  these  statements  mean  exactly  the  same  thing.  En- 
gineers use  the  first  two  expressions  for  acceleration,  while 
other  scientific  men  more  commonly  use  the  last.  two.  It 
is  convenient  to  abbreviate  "  feet-per-second  per  second " 
as  ft. /sec.2  and  "  centimeters-per-second  per  second "  as 
cm. /sec.2,  but  each  of  these  abbreviated  expressions  means 
simply  so  many  velocity  units  gained  per  second. 

The  accelerating  rates  of  cars  vary  according  to  service 
and  equipment,  but  the  following  rates  are  common  in  prac- 
tical operation  :  — 

Steam  locomotive,  freight  service,  0.1-0.2  miles-per-hr.  per  sec. 
Steam  locomotive,  passenger  service,  0.2-0.5  miles-per-hr.  per  sec. 
Electric  locomotive,  passenger  service,  0.3-0.6  miles-per-hr.  per  sec. 
Electric  car,  interurban  service,  0.8-1.3  miles-per-hr.  per  sec. 

Electric  car,  city  service,  1.5         miles-per-hr.  per  sec. 

Electric  car,  rapid  transit  service,  1.5-2.0  miles-per-hr.  per  sec. 

132.  Positive  and  negative  acceleration.     When  the  speed 
is  increasing,  the  acceleration  is  said  to  be  positive,  and  when 
the   speed   is  decreasing,  the    acceleration  is  negative.      Thus 
when  a  baseball  is  dropped  from  a  tower,  it  goes  faster  and 
faster ;    it  has  positive  acceleration.     When,  however,  it  is 
thrown  upward,  it  goes  more  and  more  slowly ;  it  has  nega- 
tive acceleration  or  retardation. 

133.  Relation  of   speed  to  time  at  constant  acceleration. 
If  we  know  the  acceleration  of  any  body,  we  can  easily  com- 
pute its  speed  at  any  time  after  it  started. 

For  example,  if  the  rate  of  acceleration  of  a  train  is  0.2  miles-per-hour 
per  second,  how  fast  is  it  moving  one  minute  after  it  starts?  One  minute 
equals  60  seconds.  If  the  train  gains  0.2  miles-per-hour  every  second, 
then  its  speed,  60  seconds  after  starting,  would  be  60  times  0.2,  or  12 
miles  per  hour. 

LAW  I.  If  the  acceleration  is  constant,  the  speed  acquired 
is  directly  proportional  to  the  time. 

Final  velocity  =  acceleration  x  time. 

v  =  at  (I) 


ACCELERATED  MOTION  137 

PROBLEMS 

(Assume  constant  acceleration.) 

1.  Express  32  feet-per-second  per  second  in  miles-per-hour  per  second. 

2.  A  body  has  a  speed  of  16  feet  per  second  at  a  certain  instant,  and 
3  seconds   later  it  has  a  speed  of   112  feet  per  second.     What  is  its 
acceleration  ? 

3.  A  train  starting  from  rest  has,  after  33   seconds,  a  speed  of   15 
miles  an  hour.     What  is  the  average  acceleration, 

(a)  In  miles-per-hour  per  second? 

(b)  In  feet-per-second  per  second? 

4.  If  a  locomotive  can  give  a  train  an  acceleration  of  5  feet-per-second 
per  second,  how  long  will  it  take,  after  slowing  down  for  a  crossing,  to 
increase  the  speed  of  the  train  from  22  feet  per  second  to  82  feet  per 
second  ? 

5.  What  is  the  acceleration  of  a  train  if  the  initial  speed  is  45  feet 
per  second,  and  after  5  seconds  the  speed  is  15  feet  per  second  ? 

6.  The  negative  acceleration  (retardation)  in  stopping  electric  trains 
is  seldom  greater  than  4  feet-per-second  per  second.     How  long  does  it 
take  to  stop  a  train  from  60  miles  an  hour? 

7.  Which  of  the  following  accelerations  is  the  largest:  — 

(a)  One  foot-per-second  per  five  seconds, 
(6)  One  foot-per-five-seconds  per  second, 

(c)  One  fifth  of  a  foot-per-second  per  second  ? 

134.    Relation  of  distance  to  time  at  constant  acceleration. 

Suppose  a  sled  gains  speed  at  a  constant  rate  as  it  goes  down 
a  hill.  If  its  acceleration  is  3  feet-per-second  per  second, 
how  far  will  it  go  in  the  first  five  seconds  after  starting 
from  rest?  We  have  already  seen  that  its  velocity  at  the 
end  of  five  seconds  will  be  5  x  3,  or  15  feet  per  second.  Now 
it  started  from  rest,  that  is,  its  initial  velocity  was  zero,  and 
gradually  its  speed  increased  until  its  final  velocity,  at  the 
end  of  5  seconds,  is  15  feet  per  second.  Therefore  its 
average  velocity  is  one  half  the  sum  of  its  initial  and  final 
velocities,  or  7.5  feet  per  second. 

Average  velocity  =  initial  velocity  +  final  velocity^ 

2 


138  PRACTICAL  PHYSICS 

We  have  already  learned  (section  129)  that  the  distance 
traversed  is  the  product  of  the  average  velocity  arid  the  time. 

So  in  this  case  the  sled  has  gone  7.5  x  5,  or  37.5  feet. 

In  general,  for  a  body  starting  from  rest,  the  average  veloc- 
ity is  one  half  the  final  velocity; 

Average  velocity  =  —  • 
2 

But  we  already  know  that  the  final  velocity  is  v  =  at ;  then, 

Average  velocity  =  —  - 
Therefore  the  distance  is 

•=f"  =  !«*  <n) 

LAW  II.  If  the  acceleration  is  constant,  the  distance  trav- 
ersed from  rest  varies  as  the  square  of  the  time. 

In  using  this  law,  acceleration  should  be  expressed  in 
ft. /sec.2  or  m./sec.2  or  cm. /sec.2,  and  t  in  seconds. 

135.  Relation  of  speed  to  distance  at  constant  acceleration. 
Suppose  we  wished  to  know  how  far  the  rapid  transit  electric 
car  mentioned  in  the  table  in  section  131  would  have  to  run 
to  develop  a  speed  of  30  miles  an  hour,  starting  from  rest. 
Since  the  question  is  concerned  only  with  speed,  distance,  and 
acceleration,  it  is  convenient  to  have  an  equation  involving 
only  v,  s,  and  t. 

From  equation  (I),  we  have 


, 

a 


and  from  equation  (II), 


2  2 

Then,  v*  =  2  as-  (III) 

LAW  III.     If  the  acceleration  is  constant,  the  speed  varies  as 
the  square  root  of  the  distance  traversed. 


ACCELERATED  MOTION  139 

Equation  (III)  enables  us  to  answer  the  question  about  the 
electric  car. 

v  =  30  miles  per  hour  =  44  feet  per  second. 
a=(say)   2.0   miles-per-hour  per  second  =  2.93  feet-per- 
second  per  second. 

s  =  —  =      442      =  330  feet. 
2  a      2x2.93 

Notice  that  30  miles  per  hour  and  2.0  miles-per-hour  per 
second  could  not  be  substituted  directly,  because  two  differ- 
ent kinds  of  time  units,  namely  hours  and  seconds,  are  in- 
volved. This  is  an  example  of  the  general  rule  that  all  the 
quantities  substituted  in  any  equation  must  first  be  expressed 
in  consistent  units. 

It  will  save  time  to  memorize  equations  (I),  (II),  and  (III). 
Notice  that  there  is  an  equation  for  each  pair  of  quantities  v 
and  £,  s  and  £,  and  v  and  s.  Alivays  use  the  one  equation  that 
gives  what  is  wanted  directly  from  the  data. 

136.  Negative  acceleration.  Suppose  that  an  engineer, 
running  at  50  miles  an  hour,  sees  a  child  on  the  track  200 
yards  ahead.  If  his  emergency  air  brakes  can  give  him  a  re- 
tardation of  4  feet-per-second  per  second,  can  he  stop  in  time  ? 

Here  we  have  a  problem  in  retardation  or  negative  accelera- 
tion. Let  us  think  of  the  problem  the  other  way  around. 
Evidently  if  the  engineer  could  stop  within  a  given  distance 
at  a  given  retardation,  he  could  get  up  speed  within  the  same 
distance  with  an  equally  great  acceleration.  So  we  may  ask 
instead,  whether  the  engineer  could  get  up  to  a  speed  of  50 
miles  an  hour  within  200  yards,  if  accelerating  at  4  feet-per- 
second  per  second.  The  answers  to  the  two  questions  are 
the  same. 

Since  the  quantities  involved  are  a  velocity  v,  and  a  dis- 
tance s,  we  will  use  equation  (III). 

v  =  50  miles  an  hour  =  73.3  ft. /sec. 
a  =  4  ft./sec.2. 


140  PRACTICAL  PHYSICS 


Then  «  =     -  =  =672  feet  =  224  yards. 

2a        2x4 

So  the  engineer  could  not  stop  in  time. 

PROBLEMS 

(Assume  constant  acceleration.) 

1.  If  a  locomotive  can  give  its  train  an  acceleration  of  5  feet-per-sec- 
ond  per  second,  in  what  distance  can  it  develop  a  speed  of  60  feet  per 
second,  starting  from  rest  ? 

2.  A  boy  runs  toward  an  icy  place  in  the  sidewalk  at  a  speed  of  20  feet 
per  second  and  slides  on  it  16  feet.     What  is  the  (negative)  acceleration? 

3.  How  far  will  a  marble  travel  down  an  inclined  plane  in  3  seconds, 
if  the  acceleration  is  50  centimeters-per-second  per  second? 

4.  A  motor  cycle  starting  from  rest  acquires  a  velocity  of  40  miles  an 
hour  in  2  minutes.      What  is  the  acceleration   in   miles-per-hour  per 
second? 

5.  How  many  yards  does  the  motor  cycle  have  to  run  in  problem  4  ? 

6.  Two  suburban  stations  are  2700  feet  apart  on  a  straight  track. 
The  greatest  practicable  acceleration  or  retardation  is  3  feet-per-second 
per  second.     If  there  is  no  limit  to  the  speed  en  route,  what  is  the  short- 
est possible  running  time  between  the  stations,  with  stops  at  both  ? 

137.  Falling  is  motion  at  constant  acceleration.  It  is  pos- 
sible to  determine  in  the  laboratory  the  time  it  takes  a  body 
to  fall  various  distances.  The  results  of  an  actual  series  of 
such  experiments  are  as  follows  :  — 

DISTANCES  TIMES  RATIO  OF  TIMES 

36  cm.  0.272  sec.  3 

64  0.363  4 

100  0.452  5 

144  0.542  6 

It  will  be  seen  that  these  distances  vary  almost  exactly  as 
the  squares  of  the  times,  which  we  have  seen  to  be  the  case 
when  the  acceleration  is  constant  (see  law  II).  Therefore 
falling  is  a  case  of  motion  at  constant  acceleration. 

A  freely  falling  body  acquires  velocity  so  rapidly  that  it 
is  difficult  to  make  observations  upon  it  directly.  Long  ago 


ACCELERATED  MOTION  141 

Galileo  hit  upon  the  plan  of  studying  the  laws  of  falling 
bodies  by  letting  a  ball  roll  down  an  incline.  In  this  way 
he  "diluted"  the  force  of  gravity  and  increased  the  time  of 
fall  so  that  it  could  be  measured  more  accurately. 

138.  Galileo's  experiment  on  the  inclined  plane.     Galileo 
cut  a  trough  one  inch  wide  in  a  board  12  yards  long,  and 
rolled  a  brass  ball  down  the  trough.     After  about  one  hun- 
dred trials  made  for  different  inclinations  and  distances,  he 
concluded  that  the  distance  of  descent  for  a  given  inclination 
varied  very  nearly  as  the  square  of  the  time.     It  is  remark- 
able that  he  was  so  successful  in  this  experiment  when  we 
consider  how  he  measured  the  time.     He  attached  a  very 
small  spout  to  the  bottom  of  a  water  pail  and  caught  in  a  cup 
the  water  that  escaped  during  the  time  the  ball  rolled  down 
a  given  distance.      Then  the  water  was  weighed  and  the 
times  of  descent  were  taken  as  proportional  to  the  ascertained 
weight. 

These  experiments  of  Galileo  are  especially  interesting 
because  they  led  him  to  change  his  theories  about  the  dis- 
tance and  time  of  falling  bodies.  He  seems  to  have  been 
one  of  the  first  of  the  ancient  philosophers  who  thought  it 
worth  while  to  subject  his  theories  to  the  test  of  experiment. 

139.  All  freely  falling  bodies  have  the  same  acceleration. 
Before  the  time  of  Galileo  (1564-1642)  people  believed  that 
heavy  objects  fell  faster  than  light  objects;  in  other  words, 
that  the  speed  of  a  falling  body  depended  upon  its  weight. 
But  he  claimed  that  all  bodies,  if  unimpeded  by  the  air,  fell 
the  same  distance  in  the  same  time,  and  that  the  only  thing 
that  caused  some  objects,  like  pieces  of  paper  or  feathers,  to 
fall  more  slowly  than  pieces  of  metal  or  coins,  was  the  re- 
sistance of  the  air.     To  convince  his  doubting  friends  and 
associates  he  caused  balls  of  different  sizes  and  materials  to 
be  dropped  at  the  same  instant  from  the  top  of  the  leaning 
tower  of  Pisa.      They  saw  the  balls  start  together,  and  fall 
together,  and  heard  them  strike  the  ground  together.     Some 


142 


PRACTICAL  PHYSICS 


were  convinced,  others  returned  to  theii" 
rooms  to  consult  the  books  of  the  old  Greek 
philosopher,  Aristotle,  distrusting  the  evi- 
dence of  their  senses. 

Later  when  the  vacuum  pump  was  in- 
vented, the  truth  of  Galileo's  view  was 
confirmed  by  dropping  a  feather  and  a  coin 
in  a  vacuum  tube. 

If  we  place  a  piece  of  metal  and  some  light  object, 
like  a  bit  of  paper  or  pith,  or  a  feather,  in  a  long 
tube  (Fig.  134),  and  pump  out  the  air,  we  find  that, 
when  we  suddenly  invert  the  tube,  the  two  objects 
fall  side  by  side  from  the  top  to  the  bottom.  If  we 
open  the  stopcock,  letting  the  air  in  again,  and 
repeat  the  experiment,  we  find  that  the  metal  falls 
to  the  bottom  first. 

140.  Value  of  acceleration  of  gravity.  It 
FIG.  134.  —  Feather  is  possible  to  determine  the  value  of  the 
acceleration  of  gravity  from  the  experi- 
mental  data  obtained  in  measuring  the  time 
of  a  free  fall  (section  137),  and  it  is  also  possible  to  compute 
the  value  of  this  constant  from  the  data  got  in  the  experiment 
of  rolling  a  ball  down  an  incline.  Neither  of  these  methods, 
however,  yields  as  precise  results  as  are  obtained  in  experi- 
ments with  pendulums. 

We  are  all  familiar  with  the  pendulum  as  a  means  used  to 
regulate  the  motion  of  clocks.  It  was  long  ago  discovered 
by  Galileo  that  the  successive  small  vibrations  of  a  pendulum 
are  made  in  equal  times,  and  that  the  time  of  vibration  does 
not  depend  on  the  weight  or  nature  of  the  bob,  or  the  length 
of  the  swing,  but  does  vary  directly  as  the  square  root  of  the 
length  of  the  pendulum,  and  inversely  as  the  acceleration  of 
gravity.  This  is  expressed  in  the  following  formula:  - 


ACCELERATED  MOTION 


143 


where  t  is  the  time  in  seconds  of  a  complete  vibration,  I  is 
the  length  of  the  pendulum  in  centimeters,  g  is  the  accelera- 
tion of  gravity  in  centimeters-per-second  per  second,  and 
TTIS  3.14. 

We  can  measure  t  and  I  directly  and  TT  is  known,  so  we 
may  compute  g  from  the  formula  ;  thus, 


The  value  of  the  acceleration  of  gravity  is  about  980  centi- 
meters-per-second per  second,  or  about  32.2  feet-per-  second  per 
second.  It  varies  a  little  from  place  to  place. 

Problems  about  falling  bodies  are  just  like  other  problems 
with  constant  acceleration.  In  the  equations  we  usually  rep- 
resent the  acceleration  of  gravity  by  g. 

Thus,  for  bodies  falling  freely  from  rest, 

v  =  gt, 


i?  =  2  gs. 

It  will  be  useful  to  remember  that  the  speed  with  which  a 
body  must  be  projected  upward  to  rise  to  a  given  height  is 
the  same  as  the  velocity  which  it  will  acquire  in  falling  from 
the  same  height.  (Compare  this  statement  with  section  136.) 

PROBLEMS 

(Neglect  air  resistance.) 

1.  Make  a  table  like  the  following,  running  up  to  t  =  5  seconds,  and 
fill  it  in. 


NUMBER  OF 
SECONDS,  t 

TOTAL  DISTANCE 
FALLEN,  «  (FT.) 

SPEED  AT  END 

OF  EACH  SECOND, 
v  (FT./SEC.) 

TOTAL  DISTANCE 
FALLEN, 
«  (METERS) 

SPEED  AT  END 
OF  EACH  SECOND, 
t>  (M./SEC.) 

1 

16.1 

32.2 

4.9 

9.8 

2 

? 

? 

? 

v 

144  PRACTICAL  PHYSICS 

2.  A  stone  is  dropped  from  the  top  of  a  cliff  and  strikes  at  the  base 
in  5  seconds,     (a)  What  velocity  did  it  acquire  ?     (b)  How  high  is  the 
cliff? 

3.  If  a  falling  body  has  acquired  a  velocity  of  150  feet  per  second, 
how  long  has  it  been  falling  ?     How  far  ? 

4.  How  many  centimeters  does  a  stone  fall  in  0.5  seconds  ? 

5.  How  many  centimeters  does  a  stone  fall  during  the  fifth  second? 

6.  A  rifle  is  fired  straight  up  (for  speed,  see  table  in  section  129). 
How  long  before  the  bullet  comes  down  again  ?     How  high  will  it  go  ? 
(Assume  that  air  resistance  is  negligible,  which  is  far  from  true.) 

7.  A  baseball  is  thrown  up  in  the  air  and  reaches  the  ground  after 
4  seconds.     How  high  did  it  rise  ? 

8.  The  weight  of  a  pile  driver  drops  5  feet  at  first  and  later  15  feet. 
How  much  faster  is  it  moving  when  it  strikes  in  the  latter  case  than  in 
the  first  case  ? 

9.  A  body  is  thrown  vertically  upward  with  a  velocity  of  50  meters 
per  second.     With  what  velocity  will  it  pass  a  point  100  meters  from  the 
ground  ?      (HiNT.  —  How  high  does  the  body  rise  ?) 

10.  How  long  would  it  take  a  bomb  to  fall  1000  feet  from  an  aero- 
plane? During  the  fall  the  bomb  would  continue  to  move  sidewise  with 
the  same  velocity  as  the  aeroplane,  and  so  would  always  be  directly  under 
it.  If  the  speed  of  the  aeroplane  is  60  miles  an  hour,  how  far  will  the 
bomb  move  sidewise  while  it  is  falling? 


Speed  = 


SUMMARY   OF  PRINCIPLES   IN   CHAPTER  VII 
distance 


time 


Acceleration  =  gain  in  speed  , 
time 

Laws  of  motion  at  constant  acceleration  :  — 

I..    v=at, 


m.  i^  =  2  as. 
Value  of  acceleration  of  gravity  :  — 

0=  32.2  ft/sec.2  =  980  cm./sec.2. 


ACCELERATED   MOTION  145 


QUESTIONS 

1.  If  you  take  two  sheets  of  paper  of  the  same  size,  and  roll  one  of 
them  into  a  ball,  and  let  both  the  ball  and  the  sheet  of  paper  fall  at  the 
same  instant  from  the  same  height,  what  is  the  result?     Why? 

2.  How  mtfst  the  pendulum  bob  be  moved  on  a  clock  which  is  run- 
ning too  fast  ? 

3.  What  takes  the  place  of  a  pendulum  in  a  watch  ? 


CHAPTER   VIII 

FORCE  AND   ACCELERATION 

Inertia  —  the  fundamental  proportion  —  action  and  reaction  —  mass. 

141.  Newton's  laws  of  motion.     We  are  studying  motion, 
and  so  far  we  have  considered  how  bodies  move ;  that  is,  we 
have    been  describing  different   motions,  such  as  motion  at 
constant  speed  and  motion  at  constant  acceleration.     Now 
we  shall  begin  to  study  why  bodies  move ;  we  shall  try  to 
explain  different  motions  by  studying  the  forces  that  cause 
them.     Practically  all  that  we  know  about  this  part  of  physics 
dates  back  to  Sir  Isaac  Newton  (1642-1727),  who  wrote  a 
treatise  on  the  principles  (Principia)  of  natural  philosophy 
or  physics.     His  whole  book,  and  indeed  all  mechanics  since 
his  day,  is  based  on  three  very  simple  laws,  called  Newton's 
laws.     The  first  of  them  is  the  law  of  inertia,  the  second  the  law 
of  acceleration,  and  the  third  the  law  of  interaction.     These  will 
now  be  discussed  in  turn. 

142.  First  law  —  Inertia.     It  is  a  familiar  fact  that  nothing 
in  nature  will  either  start  or  stop  moving  of  itself.     Some 
force  from  outside  is  always  required.     For  example,  a  horse 
when  starting  a  wagon,  even  on  an  excellent  road,  has  to 
pull  very  hard  at  first ;  once  the  wagon  is  going,  the  horse 
can  keep  it  moving  with  very  little  effort ;  but  if  he  tries  to 
stop  it  to  avoid  running  over  some  one,  he  has  to  push  back 
hard.     So  also  when  a  moving  ship  collides  with  another  ship 
or  a  dock,  it  requires  an  enormous  retarding  force  to  stop 
her.     In  1908  the  Florida  rammed  the  Republic,  and  her  bow 
was  crumpled  back  30  feet  before  the  force  stopped  her. 

146 


SIR  ISAAC  NEWTON.  Born  in  England,  in  1612.  Died  in  1727,  and  is  buried  in 
Westminster  Abbey.  Founded  the  science  of  mechanics,  and  made  many  im- 
portant discoveries  in  light.  Famous  also  for  his  achievements  in  mathe- 
matics and  astronomy. 


FORCE  AND  ACCELERATION 


147 


This  inability  of  matter  to  change  its  state  of  motion  (or  of 
rest),  except  it  be  influenced  from  outside,  is  called  inertia. 

We  may  illustrate  this 
property  of  inertia  by  bal- 
ancing a  card  on  a  finger 
with  a  coin  on  top.  Then 
we  may  snap  the  card  out, 
leaving  the  coin  on  the 
finger.  The  coin  moves 
only  a  little  because  there 
is  only  a  small  force  due 
to  friction  to  get  it  started. 
This  may  also  be  done 
with  the  apparatus  shown 
in  figure  135. 

Another  interesting  experiment  is  to  try 
to  pick  up  a  flatiron  by  means  of  a  linen 
thread  tied  to  it  (Fig.  136).  If  we  pull  slowly, 
we  may  be  able  to  do  this,  but  if  we  pull  with 
a  jerk,  the  string  always  breaks,  because  so 
much  extra  force  is  required  to  set  the  flat- 
iron  in  motion  quickly. 


Fia.  135.  — Inertia 
keeps  the  ball 
from  moving. 


I 

FIG.  136.  —  Inertia  holds  the 
weight  still. 

This  familiar  fact  that  bodies  act  as 

if  disinclined  to  change  their  state,  whether  of  rest  or  motion, 
was  expressed  by  Newton  in  the  following  way:  — 

LAW  I.  Every  body  persists  in  a  state  of  rest,  or  of  uniform 
motion  in  a  straight  line,  unless  compelled  by  external  forces  to 
change  that  state. 

QUESTION 

If  you  roll  a  ball  along  the  ground,  it  does  not  keep  going  indefinitely. 

An  automobile  can  start  by  itself. 

Do  these  facts  controvert  Newton's  First  Law? 

143.  Applications  of  inertia.  A  nail  can  easily  be  driven 
into  a  heavy  piece  of  wood,  even  when  the  wood  does  not  lie 
on  a  firm  foundation,  because  the  quick  blow  of  a  hammer 
does  not  set  the  heavy  piece  of  wood  in  motion •  to  any  great 


148 


PRACTICAL  PHYSICS 


FIG.  137.  —  Inertia  of  sledge  hammer. 


extent.  It  is  very  difficult,  however,  to  drive  a  nail  through 
a  light  stick  unless  the  stick  is  placed  upon  a  solid  foundation, 
or  unless  the  stick  is  steadied  by  the  inertia  of  a  heavy  sledge 
hammer,  as  shown  in  figure  137. 

When  the  head  of  a  hammer  comes  off,  the  best  way  to 

drive  it  on  again  is  to 
hit  the  other  end  of  the 
handle,  rather  than  the 
head,  against  some  solid 
foundation  or  with  an- 
^  other  hammer.  (Why  ?) 
144.  Inertia  in  curved 
motion.  This  tendency  of 
a  body  to  continue  to 
move  in  a  straight  line  is  very  evident  when  it  is  desirable  to 
make  the  body  move  in  a  circle.  In  this  common  case,  a 
force  is  required  to  pull  the  body  in  toward  the  center  of  the 
circle,  so  that  it  may  not  fly  off  on  a  tangent.  Such  a  force  is 
called  a  centripetal  force,  mean- 
ing a  force  directed  toward 
the  center. 

When  an  athlete  swings  a 
16-pound  hammer  around  his 
head  before  throwing  it,  he 
has  to  pull  it  inward  because 
of  its  inertia.  When  he  stops 
pulling  inward,  it  flies  off  on 
a  tangent.  So  all  he  has  to 
do  to  throw  it  is  to  let  go. 


FIQ.   138.  —  Mud  flies  off  on  a  tangent. 


Emery  wheels  revolve  very 
rapidly.  Sometimes  one 
bursts  because  the  cohesion  between  its  parts  is  not  enough  to 
supply  the  centripetal  force_ necessary  to  keep  these  various 
parts  moving  in  their  respective  circles. 

The  mud  on  a  bicycle  wheel  stays  on  the  wheel  only  if  the 


FORCE  AND  ACCELERATION  149 

adhesion  between  it  and  the  tire  is  great  enough  to  pull  it 
around  with  the  tire ;  otherwise  it  flies  off  on  a  tangent. 

In  a  cream  separator  the  denser  part  of  the  milk  gets  out- 
side and  crowds  the  lighter  cream  inward.  This  is  because 
the  greater  inertia  of  the  milk  (that  is,  its  greater  tendency 
to  move  along  a  tangent)  prevails  over  that  of  the  cream. 

When  a  train  goes  around  a  curve,  the  flanges  of  the  wheels 
are  pressed  inward  by  the  outer  rail ;  if  the  rail  is  not  strong 
enough  to  exert  the  necessary  force  inward,  the  train  is 
wrecked  on  the  outside  of  the 
roadbed.  This  is  made  clear 
in  figure  139.  The  weight  of 
the  train  is  balanced  by  the 
upward  push  A  of  the  tracks, 
the  centripetal  force  B  is  ex- 
erted inward  by  the  rails 
against  the  flanges,  and  there- 
fore the  resultant  R  is  in- 
Clined.  Consequently  the  FIG.  139. -Banking  rail,  on  a  carve. 

track  should  be  tilted  toward  the  center,  that  is,  "  banked," 
so  as  to  be  at  right  angles  to  R.  This  equalizes  the  pressure 
on  both  sides  and  relieves  the  pressure  on  the  outside  flanges, 
thus  making  them  less  likely  to  break. 

145.  Second  law  —  Acceleration.  We  have  been  discussing 
what  happens  to  a  body  when  forces  do  not  act  on  it.  Let 
us  now  consider  what  happens  when  forces  do  act  on  it. 

Whenever  an  "  unbalanced  "  force  is  acting  on  a  body,  the 
body  has  an  acceleration  in  the  direction  in  which  the  force 
acts,  and  the  acceleration  is  proportional  to  the  force.  By 
an  unbalanced  force  we  mean  more  push  or  pull  in  one  direction 
than  in  the  other.  For  example,  a  locomotive  is  pulling  a 
train  at  a  constant  speed  of  50  miles  an  hour.  The  engine 
is  certainly  exerting  a  force  on  the  train,  but  there  are  other 
forces,  due  to  friction  and  air  resistance,  acting  in  the 
opposite  direction,  and  these  just  balance  the  pull  of  the 


150  PRACTICAL  PHYSICS 

engine.  The  net  force  forward  is  zero  ;  if  it  was  not  zero\ 
the  train  would  not  only  be  going  forward  but  accelerating 
forward  ;  it  would  be  gaining  speed. 

It  is  important  to  keep  in  mind  that  it  is  net  force  and  acceleration 
which  always  go  together,  and  not  net  force  and  motion.  The  above 
example  shows  that  we  can  have  motion  without  net  force  if  the  speed 
is  not  changing. 

.  LAW  II.  The  acceleration  of  a  given  body  is  proportional  to 
the  force  causing  it. 

That  is,  if  any  given  body  is  acted  on  at  one  time  by  a 
force  Fv  and  at  another  time  by  another  force  jP2,  then 


where  al  and  a2-are  the  accelerations  produced  by  F^  and  F2. 

In  other  words,  if  we  pull  a  body  with  a  certain  force,  and 
at  another  time  pull  it  twice  as  hard,  it  will  have  twice  as 
much  acceleration  the  second  time  as  the  first. 

One  way  to  cause  a  force  to  act  on  a  body  is  to  let  the 
body  fall.  In  this  case  the  force  acting  is  known,  namely, 
the  weight  TFof  the  body.  The  acceleration  is  also  known, 
namely,  #,  which  is  32.2  feet-per-second  per  second,  or  980 
centimeters-per-second  per  second.  So  the  weight  of  the 
body  and  its  acceleration  when  falling  can  always  be  used 
as  two  of  the  numbers  in  a  proportion. 

That  is,  -*.f. 

This  enables  us  to  compute  the  force  needed  to  give  a 
certain  body  any  desired  acceleration. 

For  example,  a  freight  train  weighs  1000  tons.  How  great  a  force 
is  necessary  to  give  it  an  acceleration  of  half  a  foot-per-second  per  second  1 

F    _  0.5 
1000  ~  32.2' 

1000  x  0.5 


32.2 


^ 


FORCE  AND  ACCELERATION  151 

146,  Units.  In  the  equation  F/W=a/g,  it  makes  no 
difference  in  what  unit  F  and  W  are  expressed,  provided 
only  that  both  are  expressed  in  the  same  unit.  Both  can  be 
expressed  in  pounds,  or  in  ounces,  or  in  tons,  or  in  kilograms, 
or  in  grams,  or  in  a  less  familiar  unit  called  a  "  dyne."  The 
dyne  is  a  very  small  unit  of  force  much  used  in  scientific 
work,  especially  electrical  measurements.  It  can  be  defined  as 
1/980  of  a  gram  weight.*  It  is  about  the  weight  of  a  milli- 
gram. If  a  force  is  given  in  terms  of  any  one  of  these  units, 
it  can  be  expressed  in  terms  of  any  other  of  them  with  the 
help  of  the  following  table:  - 

1  gram    =  980  dynes.  1  dyne  =  0.00102  grams. 

1  pound  =  454  grams.  1  gram  =  0.00220  pounds. 

1  pound  =  445,000  dynes.  1  dyne  =  0.00000225  pounds. 

Similarly  a  and  g  may  be  in  any  units,  provided  only  that 
both  are  in  the  same  unit.  If  both  are  to  be  in  feet-per-second 
per  second,  the  numerical  value  of  g  is  32.2  ;  if  both  are  to 
be  in  centimeters-per-second  per  second,  the  numerical  value 
of  g  is  980. 

PROBLEMS 

1.  Express  110  grams  in  pounds. 

2.  Express  110  grains  in  dynes. 

3.  Express  8,000,000  dynes  in  pounds. 

4.  What   acceleration  will  a  force  of   5  pounds  produce  in  a  body 
weighing  16.1  pounds? 

5.  What  acceleration  will  a  force  of  1  gram  produce  in  a  body  weigh- 
ing 327  grams  ? 

6.  What  acceleration  will  a  force   of  1   pound  produce   in  a  body 
weighing  1  pound  ? 

7.  What  acceleration  will  a  force  of  1  dyne  produce  in  a  body  weigh- 
ing 1  gram  ?     (NOTE.  — The  answer  to  this  problem  is  often  regarded  as 
the  definition  of  a  dyne.) 

8.  State  accurately  in  words  the  definition  of  a  dyne  that  is  referred 
to  in  the  last  problem. 

*  See  also  problems  7  and  8  below. 


152  PRACTICAL  PHYSICS 

9.   A  body  weighing  10  pounds  is  observed  to  have  an  acceleration  of 
2  feet-per-secoud  per  second.   .What  force  is  acting? 

10.  A  force  of  1  kilogram  is  observed  to  produce  an  acceleration  of 
9.8  centime*ters-per-secoud  per  second  in  a  certain  body.     How  much 
does  the  body  weigh? 

11.  A  force  of  1000  dynes  is  observed  to  produce  an  acceleration  of 
9.8  centimeters-per-second  per  second  in  a  certain  body.     How  many 
grains  does  the  body  weigh? 

12.  An  automobile  weighing  2   tons  is  started  from   rest  with  an 
acceleration  of  4  feet-per-second  per  second.    How  hard  is  the  road  push- 
ing the  bottoms  of  the  rear  tires  forward  ? 

13.  An  elevator  weighing  980  kilograms  is  pulled  upward  by  a  force 
great  enough  to  hold  up  the  weight  and  give  200  kilograms  of  net  force 
besides.     What  is  the  acceleration  of  the  elevator? 

14.  What  pressure  will  a  150-pound  man  exert  on  the  floor  of  an 
elevator  which  is  going  up  with  an  acceleration  of  4  feet-per-second  per 
second  ? 

15.  A  train  starting  from  rest  with  a  constant  acceleration  takes  44 
seconds  to  get  up  to  a  speed  of  30  miles  an  hour.     If  the  train  consists 
of  4  all-steel  cars,  each  weighing  with  its  load 62. 5  tons,  what  pull  is  exerted 
by  the  engine?     (HINT.  — Compute  acceleration  and  then  find  force.) 

147.  Third  law  —  Interaction.  Newton's  third  law  is  based 
on  two  familiar  facts.  One  way  of  stating  the  first  of  these 
facts  is  that  there  can  never  be  a  force  acting  in  nature  unless 
two  bodies  are  involved,  one  exerting  it  and  one  on  which  it 
is  exerted.  Thus,  when  a  railroad  train  is  pulled,  there  is  an 
engine  that  does  the  pulling  ;  and  on  the  other  hand,  the 
engine  cannot  exert  a 'pull  or  a  push  without  something 
to  be  pvlled  or  pushed.  An  electric  car  or  an  automobile 
seems,  perhaps,  to  push  itself  along,  but  really  the  track  or  the 
road  under  the  wheels  is  exerting  a  force  on  the  wheels 
and  pushing  the  car  along.  We  have  all  seen  what  happens 
when  the  car  track  is  so  icy  or  the  road  so  muddy  that  it 
cannot  push  on  the  wheels.  The  motor  is  going  just  as  hard 
as  ever,  but  the  car  does  not  move. 

In  order  to  make  this  idea  seem  more  real  to  us,  let  us  try  the  experi- 
ment on  a  small  scale,  as  shown  in  figure  140.  If  we  wind  up  the  little  toy 
engine,  and  place  it  on  the  circular  track,  which  is  so  mounted  as  to  turn 


FORCE  AND  ACCELERATION  153 

easily,  we  find  that  the  track  turns  around  and  the  rails  under  the 
wheels  go  backwards.  If  we  hold  the  track  fast,  the  engine  goes  ahead 
twice  as  fast  as  at  first,  and  if  we  hold  the  engine  fast,  the  track  turns 
around  backwards  twice  as  fast  as  at  first. 

Another  case  is  that  of  any  heavy  object :  there  is  a  force 
called  its  weight  (force  of  gravity)  pulling  it  down  ;  but  we 
know  that  it  is  the  earth  that  exerts  this  force. 


FIG.  140.  — Track  pushes  the  engine  forward. 

This,  then,  is  the  first  fact  :  whenever  there  is  a  force  in 
nature  there  must  be  two  bodies,  one  to  exert  it  and  one  to 
receive  it. 

But  we  can  go  farther  than  this.  We  can  say  that  when- 
ever there  is  a  force  in  nature,  there  must  be  not  only  two 
bodies  involved,  but  another  force.  That  is,  forces  never 
exist  singly,  but  always  in  pairs.  If  the  first  force  was 
exerted  by  a  locomotive  on  a  train,  the  second  will  be  exerted 
by  the  train  on  the  locomotive.  The  train  will  pull  back  on 
the  locomotive  just  as  hard  as  the  locomotive  pulls  forward 
on  the  train.  If  a  road  is  pushing  forward  on  the  wheels  of 
the  automobile,  the  wheels  must  be  pushing  back  on  the  road. 

If,  instead  of  the  road,  we  substitute  great  rollers,  we  may  measure  this 
backward  push.  This  is  the  method  sometimes  used  in  testing  labora- 
tories in  making  power  tests  of  automobiles  and  locomotives. 


154  PRACTICAL  PHYSICS 

Finally,  when  any  heavy  object  is  pulled  downward  by  the 
earth,  the  heavy  object  must  be  pulling  the  earth  up  with  an 
equal  force.  This  does  not  seem  very  likely  at  first,  but 
this  is  simply  because  the  force  is  so  small  and  the  earth  so 
large  that  the  force  has  an  imperceptible  effect  on  the  earth. 
If  the  heavy  body  which  we  are  thinking  of  is  the  moon, 
the  whole  thing  becomes  reasonable  at  once,  for  the  earth  and 
the  moon  are  actually  rotating  about  a  point  0  (Fig.  141), 

which  is  not  ex- 
actly at  the  center 
of  the  earth.  So 
the  moon  must 
continually  pull 
the  earth  to  make 
MOON  ^s  center  of  grav- 
ity move  in  its 
circle. 
EARTH  This  fact  that 

FIG.  141.  —Rotation  of  the  moon  about  the  earth.         f  , 

forces  always 

occur  in  pairs,  one  of  the  pair  being  equal  and  opposite  to  the 
other,  was  expressed  by  Newton  in  the  following  form  :  - 

LAW  III.  With  every  action  (or  force)  there  is  an  equal 
and  opposite  reaction. 

148.  Mass  vs.  weight.  "  Mass "  and  "  weight  "  are  con- 
stantly confused  in  ordinary  conversation.  While  we  have 
preferred  not  to  use  the  term  "mass"  in  studying  Newton's 
second"  law,  yet  it  is  well  to  know  its  precise  meaning  that 
we  may  read  intelligently  the  books  which  make  use  of  it. 

Mass  means  quantity  of  matter.  It  is  the  answer  to  the 
question,  "  How  much  matter  is  there  in  a  given  body  ?  " 

Weight  means  the  pull  of  gravity  on  the  body.  The 
weight  of  a  body  is  &  force  acting  on  the  body,  not  a  descrip- 
tion of  what  it  contains. 

The  unit  of  mass  is  the  quantity  of  matter  contained  in  a 
certain  piece  of  platinum  (the  standard  kilogram,  Fig.  142). 


FORCE  AND  ACCELERATION 


155 


The  unit  of  weight  is  the  pull  of  the  earth  on  that  same 
piece  of  platinum,  when  it  is  near  sea  level  and  at  latitude  45°. 

Since  a  kilogram  mass  weighs  a  kilogram  under  these 
standard  conditions,  the  mass  and  the  "  standard  weight "  of 
a  body  are  numerically  equal. 
But  if  we  carry  a  kilogram 
mass  to  the  top  of  a  high 
mountain,  and  weigh  it  on  a 
very  sensitive  spring  balance, 
it  will  weigh  less  than  a  kilo- 
gram, because  it  is  farther 
from  the  center  of  the  earth, 
and  so  the  earth  pulls  less 
hard  on  it.  The  reading  of 
the  spring  balance  might  be 
called  its  "local  weight." 

Since  all  bodies  on  the 
mountain  top  would  weigh 
less  in  the  same  proportion, 
we  can  get  the  standard  weight  of  anything  without  de- 
scending the  mountain  by  weighing  it  on  an  equal-arm  bal- 
ance against  a  set  of  "standard  weights."  This  is  what  we 
always  do  in  the  laboratory  and  in  the  outside  world  when 
we  want  to  know  weights  accurately.  So  when  we  speak  of 
the  weight  of  a  body  we  almost  always  mean  its  "  standard 
weight." 

W 

Since  F  = — a,  and  since  the  standard  weight  W  and  the 

9 

mass  M  are  numerically  equal,  we  shall  get  the  same  value 

for  F  if  we   write    (when   using   grams,    centimeters,  and 
seconds) 


FIG.  142.  — Standard  kilogram. 


980' 


or 


156  PRACTICAL  PHYSICS 

Here  F  is  in  grams;  if  we  choose,  however,  to  express  the 
force  as  F'  dynes,  instead  of  as  F  grams,  then  F  and  F'  will 
be  different  numbers,  and 

F1  =  980  F, 
so  F'  (dynes)  =  M (grams)  x  a  (cm. /sec.2). 

This  is  a  common  way  of  expressing  Newton's  second  law. 

SUMMARY   OF  PRINCIPLES   IN  CHAPTER  VIII 
Newton's  laws  and  the  fundamental  proportion :  — 

I.  Every  body  continues  in  a  state  of  rest  or  of  uniform 
motion  in  a  straight  line,  unless  compelled  by  external 
forces  to  change  that  state. 

II.  The  acceleration  of  a  given  body  is  proportional  to  the 
force  causing  it. 

—  =  - 
W~ g 

III.  With  every  action  (or  force)  there  is  an  equal  and  opposite 
reaction. 

Distinction  between  mass  and  weight 

QUESTIONS 

1.  How  is  the  water  quickly  removed  from  wet  clothes  in  a  steam 
laundry? 

2.  Why  does  a  train  continue  to  move  after  the  steam  is  shut  off  ? 

3.  Why  do  automobiles  "  skid"  in  rounding  corners  rapidly? 

4.  What  does  an  aviator  have  to  do  to  round  a  corner  safely,  and 
why? 

5.  Why  can  small  emery  wheels  be  safely  driven  at  a  greater  speed, 
that  is,  at  more  revolutions  per  minute,  than  larger  ones  ? 

6.  Why  does  a  wheel,  or  any  revolving  part  of  a  machine,  sometimes 
shake  or  hammer  in  its  bearings? 

7.  Explain  how  a  locomotive   engineer  can  tell,  when   he  starts  up 
his  train,  if  one  of  the  cars  has  been  uncoupled  from  the  train. 

8.  Explain  why  lawn  sprinklers  rotate.     Would  such  a  sprinkler  ro- 
tate in  a  vacuum  ? 


CHAPTER   IX 

ENERGY   AND   MOMENTUM 

Kinetic  energy  —  the  law  of  energy  —  potential  energy  —  the 
conservation  of  energy — momentum  and  its  law. 

149.  Kinetic  energy.  We  have  already  seen  (section  31) 
that  in  physics  work  involves  not  only  force  but  also  dis- 
placement. Whenever  a  force  moves  anything  in  its  own 
direction,  the  force  does  work  on  the  thing,  and  when- 
ever anything  moves  against  a  force,  the  thing  does  work 
against  the  force. 

The  energy  of  anything  may  be  defined  as  its  capacity  for 
doing  work.  Thus  a  heavy  flywheel  will  keep  machinery 
running  for  some  time  after  the  power  has  been  shut  off. 
Therefore,  a  heavy  flywheel  in  motion  can  do  work;  it  has 
energy.  The  energy  of  any  body  which  is  due  to  its  motion 
is  called  kinetic  energy. 

Let  us  consider  more  carefully  the  case  of  a  heavy  flywheel 
on  an  engine.  At  first  the  engine  has  to  push  and  pull  on  the 
crank  shaft  to  get  the  flywheel  started  and  to  bring  it  up  to 
speed;  the  engine  has  to  do  work  on  the  flywheel.  When 
once  the  flywheel  is  up  to  speed,  however,  the  engine  does 
not  have  to  push  or  pull  any  longer  to  keep  the  flywheel 
going  (except  for  friction,  which  we  will  neglect  for  the 
moment).  From  this  time  on  all  the  work  that  the  engine 
does  goes  into  the  driven  machinery  attached  to  the  shaft. 
Suppose  now  that  the  pressure  of  the  steam  on  the  engine 
suddenly  drops,  or  that  an  extra  load  is  thrown  on  the  shaft. 
The  shaft  does  not  stop  turning  suddenly,  or  drop  instantly 
to  a  lower  speed.  It  slows  down  gradually,  pulling  back  on 

157 


158  PRACTICAL  PHYSICS 

the  flywheel  as  it  does  so,  and  taking  work  out  of  the  fly- 
wheel, that  is,  making  the  flywheel  do  work  instead  of 
absorbing  it.  This  continues  until  the  engine  picks  up  the 
load  again,  or  until  the  flywheel  stops. 

In  other  words,  the  flywheel,  as  long  as  it  is  moving,  can 
do  work  on  the  shaft  if  necessary,  and  the  faster  it  is  moving, 
the  more  work  it  can  do  before  it  comes  to  rest.  In  physics 
we  describe  this  very  familiar  fact  by  saying  that  the  fly- 
wheel has  energy,  and  since  its  energy  depends  upon  its  being 
in  motion,  we  call  it  kinetic  energy,  or  energy  of  motion. 

Every  body  in  motion  has  kinetic  energy;  that  is,  it  will  do 
a  certain  amount  of  work  against  a  resisting  force  before  it 
will  stop.  Furthermore  the  kinetic  energy  of  a  body  will 
be  greater  the  heavier  it  is  and  the  faster  it  is  moving. 

150.  How  to  measure  kinetic  energy.  It  will  be  easier  to 
do  this  for  a  body  moving  straight  ahead  rather  than  in  a 
circle.  We  will  consider  first  how  much  work  it  takes  to 
get  a  heavy  body  up  to  a  given  speed,  and  then  how  much 
work  it  will  do  before  it  stops.  By  definition  this  latter  is 
its  kinetic  energy. 

The  force  necessary  to  get  a  body  started  with  a  given 
acceleration  a  is,  by  the  fundamental  proportion  (section 
145), 

W        Wn 

J1  =  — a. 

9 

If  the  distance  which  the  body  moves  before  it  gets  up  to  a 
given  speed  is  called  s,  the  work  done  is  the  product  of  the 
force  by  the  distance,  namely, 

Jk-JTi. 

9 

But  it  will  be  seen  that  the  product  as  can  be  expressed  in 
terms  of  the  speed  acquired,  v,  by  means  of  the  third  law  of 
accelerated  motion  (section  135).  Thus, 

v2  =  2  as, 


ENERGY  AND  MOMENTUM  159 


•I 

So  the  work  done  is 

Fs=  ^ 

Thus  we  see  that  the  work  required  to  bring  a  heavy 
body  from  rest  up  to  a  given  speed  does  not  depend  on  the 
acceleration,  or  on  the  distance  covered  while  coming  up  to 
speed,  but  only  on  the  weight  of  the  body  and  the  speed 
itself. 

Now,  how  much  work  will  the  body  do  against  a  retarding 
force  before  it  comes  to  rest?  We  have  already  seen  that 
the  easiest  way  to  think  of  a  retardation  problem  is  as  an 
acceleration  problem  reversed.  That  is,  a  body  will  stop 
under  a  given  retarding  force  in  the  same  distance  that  it 
would  need  to  get  up  speed  under  an  equal  accelerating  force, 
and  it  will  do  the  same  work  against  the  retarding  force 
that  an  equal  accelerating  force  would  have  to  do  on  it  to 
get  it  started.  So  the  formula  above  gives  not  only  the 
work  necessary  to  start  it,  but  also  the  work  it  will  do  when 
it  stops. 

Therefore, 

Kinetic  energy  =  —  — . 

151.  The  energy  equation.  The  equation  just  found, 
namely, 


is  called  the  energy  equation.  It  applies,  as  we  have  just 
seen,  either  to  accelerating  or  to  retarding  bodies,  if  they 
start  from  or  come  to  rest.  It  can  be  stated  in  words  as 
follows  :  — 

If  the  body  is  gaining  speed, 

Gain  of  kinetic  energy  =  accelerating  force  x  distance 
=  work  done  by  force  on  body. 


160  PRACTICAL   PHYSICS 

If  the  body  is  losing  speed, 

Loss  of  kinetic  energy  =  retarding  force  x  distance 

=  work  done  by  body  against  force. 

152.  Units.  In  using  this  equation  we  must  be  consistent 
in  our  units.  Thus  .Fand  TFare  both  forces  and  both  must 
be  expressed  in  the  same  unit  in  any  one  application  of  the 
equation.  In  one  problem  we  may  choose  tons  and  in  an- 
other dynes,  but  in  any  single  problem  all  forces  must  be  in 
tons  if  we  have  chosen  tons,  and  in  dynes  if  we  have  chosen 
dynes. 

In  the  same  way,  s,  v,  and  g  must  all  involve  the  same  unit 
of  length.  In  one  problem  we  may  choose  centimeters  and  in 
another  feet,  but  once  we  have  started  the  problem  we  must 
stick  to  our  choice. 

In  expressing  the  velocity,  v,  and  the  acceleration,  g,  it  is 
customary  always  to  use  the  second  as  the  unit  of  time. 
Therefore  g  will  always  be  either  32.2  ft. /sec.2  or  980  cm. /sec.2 
according  as  we  have  chosen  feet  or  centimeters  as  the  unit 
of  length. 

The  left-hand  side  of  the  equation,  Fs,  is  force  times  dis- 
tance, or  work,  and  so  the  right-hand  member,  which  is  equal 
to  it,  will  come  out  expressed  in  work  units.  There  are  several 
work  units  in  common  use,  such  as  the 

foot  pound  (ft.  lb.), 

foot  ton  (ft.  T.), 

gram  centimeter  (g.  cm.), 

kilogram  meter  (kg.  m.),  and 

dyne  centimeter  ("erg"). 

Since  each  of  these  work  units  is  a  force  unit  times  a  dis- 
tance unit,  we  can  always  tell  what  unit  the  kinetic  energy 
will  come  out  in,  if  we  notice  what  force  unit  and  what  dis- 
tance unit  we  started  with. 

For  example,  if  W  is  in  pounds,  v  in  feet  per  second,  and  g  in  feet-per- 
second  per  second  (#  =  32.2  ft./sec.2),  the  kinetic  energy  (Wv*/2  g}  will 


ENERGY  AND  MOMENTUM  161 

be  in  foot  pounds.  But  if  W  is  expressed  in  dynes,  v  in  centimeters  pet 
second,  and  g  in  centimeters-per-second  per  second  (g  =  980  cm.  /sec.2), 
the  kinetic  energy  (Wo*/'2g')  will  be  hi  dyne  centimeters.  There  is  a 
shorter  name  for  a  "  dyne  centimeter  "  ;  it  is  usually  called  an  erg.  Since 
the  erg  is  a  very  small  unit  of  work,  the  joule  =  107  ergs  is  often  used. 

153.  Applications  of  the  energy  equation.  The  energy  equa- 
tion will  help  us  to  solve  many  useful  problems  about  moving 
things  which  involve  the  question  "how  far,"  or  the  idea  of 
distance  in  general. 

For  example,  consider  again  the  problem  of  the  engineer  and  the 
child  (section  136).  Suppose  that  the  train  is  going  50  miles  an  hour, 
but  that  we  do  not  know  its  rate  of  retardation.  If  the  retarding  force 
is  equal  to  one  eighth  of  the  weight  of  the  train,  how  far  will  the  train 
run  before  coming  to  a  standstill? 

We  can  compute  the  rate  of  retardation  from  the  fundamental  pro- 
portion, and  then  proceed  as  before,  but  it  will  be  easier  to  use  the 
energy  equation  as  follows  :  — 

The  speed  50  miles  an  hour  =  73.3  ft./sec. 

So  the  kinetic  energy  is 


2  x  32.2 
The  retarding  force  is  W/S  Ibs. 

Therefore,  Z  x  s  = 


8        -         2  x  32.2 
and  since  the  Ws  cancel  out,  this  can  be  solved  for  s,  giving 

s  =  667  feet  =  222  yards. 
So  in  this  case  also,  the  engineer  could  not  stop  in  time. 

Again,  suppose  a  car  weighing  10  tons  is  going  36  miles  an  hour. 
What  force  is  required  to  stop  it  within  a  space  of  100  feet? 

The  velocity  must  be  expressed  in  feet  per  second  since  we  ordinarily 
do  not  use  g  in  miles/hour2. 

v  =  36  miles/hour  =  52.8  ft./sec. 
But  W  and  F  can  be  left  in  tons. 


The  kinetic  energy  is  10  x       '       =  433  ft.  T. 


So  F  x  100  =  433,  or  F  =  4.33  tons. 


162  PRACTICAL  PHYSICS 

Finally,  suppose  that  the  flywheel  mentioned  in  section  149  has  a  10 
ton  rim,  and  that  we  can  neglect  the  effect  of  the  thin  spokes.  Suppose 
also  that  it  is  16  feet  in  diameter  and  making  15  revolutions  per  minute 
(r.  p.  m.).  How  much  kinetic  energy  has  it? 

Each  part  of  the  rim  is  making  15  turns  per  minute  and  therefore 
moving  with  a  velocity  of  15  x  2  TIT  =  15  x  2  x  3.14  x  8  =  754  ft./min., 
which  is  equal  to  12.5  ft./sec.  Therefore,  the  kinetic  energy  of  the 
whole  rim  is 

10  x  (12.5)2     0,  o  f 
2x32.2    = 

This  is  the  same  as  48,600  foot  pounds.  It  is  the  amount  of  work 
which  the  flywheel  could  do  before  stopping. 

PROBLEMS 

(State  the  unit  in  which  each  answer  is  expressed.) 

1.  What  is  the  kinetic  energy  of  a  baseball  weighing  one  third  of  a 
pound  if  its  velocity  is  64.4  feet  per  second? 

2.  What  is  the  kinetic  energy  of  an  80-ton  locomotive  going  60  miles 
an  hour  ? 

3.  What  is  the  kinetic  energy  of  a  9.8-kilogram  weight  which  has 
been  falling  long  enough  to  have  a  velocity  of  12  meters  per  second? 

4.  What  is  the  kinetic  energy  of  a  16.1-gram  bullet  whose  velocity  is 
600  meters  per  second? 

5.  Find  the  kinetic  energy  in  ergs  of  a  stone  weighing  20  grams  when 
it  is  thrown  with  a  velocity  of  800  centimeters  per  second. 

6.  The  14-inch  guns  on  some  of  the  United  States  warships  fire  a 
projectile  weighing  1400  pounds  and'  are  said  to  give  it  a  "  muzzle  energy  " 
of  65,600  foot  tons.     What  is  the  velocity  of  the  projectile  as  it  leaves 
the  gun  ? 

7.  What  resistance  is  necessary  to  stop  a  body  whose  kinetic  energy 
is  90,000  ergs,  in  a  distance  of  3  meters  ? 

8.  A  boy  weighing  100  pounds  starts  to  slide  on  ice  at  a  speed  of  20 
feet  per  second.     What  is  his  initial  kinetic  energy  ?    If  the  retarding 
force  due  to  friction  is  40  pounds,  how  far  will  he  go  before  stopping? 

9.  How  great  a  force  in  excess  of  that  required  to  overcome  friction 
is  necessary  to  bring  a  3220-pound  automobile  up  to  a  speed  of  30  miles 
an  hour  in  a  distance  of  242  feet  ? 

154.  Potential  energy.  Some  things  have  a  capacity  for 
doing  work  even  when  they  are  not  in  motion.  Thus  when 
a  clock  spring  is  wound  up,  it  can  drive  the  clock  as  it  un- 


ENERGY  AND  MOMENTUM 


163 


coils,  because  of  the  elastic  strain  in  it,  due  to  its  change  of 
shape.  If  the  clock  has  a  weight  instead  of  a  spring,  the 
weight  can  drive  the  clock  because  of  its  elevated  position. 
Such  energy,  due  to  strain  or  to  position,  is  called  potential 
energy. 

Just  as  the  kinetic  energy  of  a  moving  weight  can  be 
measured  either  by  the  work  required  to  get  it  up  to  speed 
or  by  the  work  it  will  do  while  stopping,  so  the  potential 
energy*  of  a  raised  weight  or  of  a  coiled  spring  can  be  meas- 
ured either  by  the  work  required  to  raise  or  coil  it,  or  by 
the  work  it  will  do  when  it  falls  or  unwinds. 

In  a  later  chapter  we  shall  see  that  when  a  lump  of  coal 
burns,  it  gives  out  energy  in  another  form  called  heat,  some 
of  which  can  be  used  to  drive  a  steam  engine.  Thus  the 
unburned  coal  has  in  it  capacity  to  do  work,  that  is,  energy, 
and  since  this  energy  is 
not  due  to  any  motion  of 
the  lump  of  coal,  it  must 
also  be  potential.  This 
kind  of  potential  energy 
is  usually  called  chemical 
energy. 

155.  Transformation  of 
energy.  In  nature  the 
various  forms  of  energy, 
kinetic  or  potential,  are 
continually  changing  into 
one  another. 

For  example,  when  a  pen- 
dulum bob  (Fig.  143)  is  at 
the  highest  part  of  its  swing 
A,  it  has  potential  energy 
because  of  its  height.  As  it 
swings  down  this  potential  energy  disappears,  but  the  bob  gains  speed 
and  kinetic  energy.  As  the  bob  swings  up  again  on  the  other  side,  C, 
its  velocity  and  kinetic  energy  decrease,  but  its  potential  energy  increases. 


FIG.  143.  —  Transformation  of  energy  in 
pendulum. 


164  PRACTICAL  PHYSICS 

Similarly  when  coal  is  burned,  its  chemical  energy  changes  into  heat. 
Some  of  this  heat  may  be  changed  into  potential  energy  in  the  form  of 
steam  under  pressure.  A  steam  engine  could  then  change  some  of  this 
into  kinetic  energy  in  a  flywheel,  or  into  some  other  form  of  mechanical 
energy  in  a  driven  machine,  or  into  electrical  energy  in  a  dynamo. 
Some  of  this  latter  might  be  changed  into  light  in  a  lamp,  while  the  rest 
would  turn  back  to  heat. 

In  all  these  cases  we  may  think  of  energy  as  flowing  about 
from  one  place  to  another,  passing  through  the  various  ma- 
chines and  having  its  outward  appearance  changed  by  them, 
almost  like  water  flowing  from  a  reservoir  through  a  dye- 
house,  where  it  is  used  for  many  purposes,  only  finally  to  be 
dumped  into  a  stream  or  sewer,  changed  in  appearance,  but 
unmistakablythe  same  kind  of  thing  that  went  in. 

156.  The  conservation  of  energy.  After  its  use  in  the  dye- 
house  some  of  the  water  might  never  get  through  to  the 
stream,  having  been  used  up  in  some  chemical  process,  so 
that  it  is  no  longer  water.  But  in  the  case  of  energy  this 
cannot  happen.  Energy  is  never  made  from  anything  that 
is  not  energy,  or  turned  into  anything  that  is  not  energy. 
The  total  quantity  of  energy  in  the  universe  is  always  the 
same  and  is  changed 'only  in  form  and  distribution.  In  any 
given  machine  there  may  be  leaks  of  energy  because  of  fric- 
tion, radiation,  etc.,  just  as  there  may  be  leaks  in  the  pipes 
in  the  dyehouse,  but  the  energy  that  leaks  away  is  not 
destroyed,  but  is  given  as  heat  to  the  surroundings  of  the 
machine,  where  it  is  of  no  more  use  than  water  spilled  on 
the  floor. 

Thus  in  the  pendulum  (Fig.  143)  the  sum  of  the  kinetic  and  potential 
energies  is  the  same  wherever  it  is  in  its  swing,  unless  there  is  friction. 
If  there  is  friction,  some  energy  disappears  as  heat  and  less  is  left  in  the 
pendulum,  but  the  total  quantity,  counting  in  the  heat,  is  unchanged. 

This  fact,  that  energy  can  never  be  manufactured  or  de- 
stroyed, but  only  transformed,  and  directed  in  its  flow,  was  first 
stated  (although  not  very  clearly)  by  a  German,  Robert 


ENERGY  AND  MOMENTUM  165 

Mayer,  in  1842.  It  is  called  the  law  of  the  conservation  of  energy. 
It  has  become  the  most  important  generalization  in  all  physics, 
and  its  value  will  be  more  and  more  evident  as  we  study  the 
subject. 

157.  "  Perpetual  motion  "  machines.    One  of  the  most  interesting 
applications  of  this  principle  is  that  it  assures  us  that  "perpetual  motion  " 
machines  are  impossible.     Such  a  machine  would  be  one  that  runs  of  it- 
self, without  being  driven  by  an  engine,  and  without  burning  any  fuel, 
and  does  something  useful  without  cost.     Such  a  machine,  if  it  could  be 
built,  would  be  of  extraordinary  value  to  its  inventor  and  to  the  world, 
and  for  hundreds  of  years  people  have  been  trying  to  invent  one.     But 
the  principle  of  the  conservation  of  energy  shows  that  no  such  machine 
can  possibly  be  made,  because  it  would  be  manufacturing  energy  out  of 
nothing. 

158.  Momentum   and   energy.     In   the   colloquial   use  of 
these  words  there  is  a  great  deal  of  confusion.     When  a  per- 
son is  thinking  of  something  which  a  body  does  because  it 
is  moving,  he  is  likely  to  talk  about  either  its  "  momentum  " 
or  its  "  energy,"  whichever  word  first  occurs  to  him.     It  is 
therefore  worth  while  to  take  a  little  trouble  to  understand 
clearly  the  difference  between  momentum  and  energy. 

We  have  seen  that  when  a  force  acts  on  a  moving  body 
through  a  long  distance,  it  accomplishes  more  than  when  the 
distance  is  short.  The  work  done  is  greater.  It  is  also  evi- 
dent that  when  a  force  acts  on  a  moving  body  for  a  long 
time,  it  accomplishes  more  than  when  the  time  is  short.  In 
the  technioal  language  of  physics  we  say  that  the  impulse  of 
the  force  is  greater.  Impulse  may  be  defined  as  the  force 
multiplied  by  the  length  of  time  it  acts.  Thus, 

Work  =  force  x  distance, 
Impulse  =  force  x  time. 

We  shall  find  that  momentum  has  the  same  relation  to 
impulse  that  kinetic  energy  has  to  work.  The  idea  of  mo- 
mentum will  help  us  to  solve  problems  involving  "how 
long?"  just  as  the  idea  of  kinetic  energy  helps  us  to  solve 


166  PRACTICAL  PHYSICS 

problems  involving  "  how  far  ?  "  To  show  this  we  will  print 
again  the  proof  of  the  energy  equation  side  by  side  with  the 
corresponding  proof  of  a  momentum  equation. 


PROOF  OF  ENERGY  EQUATION 


But          v2  =  2  as  or  —  =  as. 


2 


So 


Wv* 
2<7 


PROOF  OF  MOMENTUM  EQUATION 


9 
But  v  —  at. 


So 


g 


The  expression  -  -  is  called  the  momentum  of  a  moving  body. 
& 

Both  kinetic  energy  and  momentum  are  proportional  to 
the  weight  of  the  moving  body ;  thus  a  railroad  train  has 
both  more  momentum  and  more  energy  than  a  motor  cycle 
running  at  the  same  speed. 

In  the  second  place  both  the  momentum  and  the  energy  of 
a  moving  body  increase  when  its  speed  increases,  but  not  ac- 
cording to  the  same  law.  The  energy  is  proportional  to  the 
square  of  the  speed.  That  is,  doubling  the  speed  of  a  train 
makes  its  kinetic  energy  four  times  as  large.  But  the  momen- 
tum is  proportional  only  to  the  first  power  of  the  speed.  That 
is,  doubling  the  speed  of  a  train  merely  doubles  its  momentum. 

Finally,  we  must  not  forget  that  there  is  a  two  (2)  in  the 
denominator  of  the  expression  for  energy,  but  not  in  the 
expression  for  momentum. 

159.    The  momentum  equation.     The  equation 

«-** 

9 

is  called  the  momentum  equation.  It  holds  either  for  accel- 
erating or  retarding  bodies,  and  can  be  expressed  in  words 
as  follows :  — 


ENERGY  AND  MOMENTUM  167 

If  the  body  is  gaining  speed, 

Gain  of  momentum  =  accelerating  force  x  time 

=  impulse  received  from  force. 

If  the  body  is  losing  speed, 

Loss  of  momentum  =  retarding  force  x  time 
=  impulse  lost  to  force. 

160.  Units  of  momentum.     In  using  the  momentum  equa- 
tion, as  in  using  the  energy  equation,  we  must  be  consistent 
in  our  units.     That  is,  _Fand  IT  must  be  in  the  same  unit  of 
force,  and  v  and  g  must  involve  the  same  unit  of  length. 
Furthermore,  v,  g,  and  t  must  all  be  expressed  in  terms  of 
seconds,  because  it  is  not  worth  while  to  remember  any  other 
way  of  expressing  g  than  32.2  ft. /sec.2  or  980  cm. /sec.2. 

The  momentum  equation  shows  that  a  momentum  Wv/g  is 
equal  to  a  force  times  a  time,  and  so  the  unit  of  momentum 
will  be  a  force  unit  times  a  time  unit.  Thus,  momentum 
may  be  expressed  as 

pound  seconds,  or 

ton  seconds,  or 

gram  seconds,  or 

kilogram  seconds,  or 

dyne  seconds, 

according  to  the  force  and  time  units  used  in  the  equation. 

The  dyne  second  as  a  unit  of  momentum  corresponds  to  the  dyne  centi- 
meter or  erg  as  a  unit  of  energy,  but  curiously  no  one  has  ever  thought 
it  worth  while  to  give  it  a  name  of  its  own  corresponding  to  "  erg." 

161.  Applications  of  the  momentum  equation.    The  momen- 
tum   equation   will  help  us  to  solve  many  problems  about 
moving  things  which  involve  the  question  "how  long?"  or 
the  idea  of  time  in  general. 

For  example,   a  certain  engine  can  exert  a  "  drawbar "  pull  on  its 
train  equal  to  ^  of  the  weight  of  the  train.     How  long  will  it  take  to 
bring  the  train  up  to  a  speed  of  50  miles  an  hour,  starting  from  rest? 
v  —  50  miles/hour  =  73.3  ft./sec. 

W \,  f  -Wx  7 
40  X  '  ~       32.2 


168  PRACTICAL  PHYSICS 

and  since  the  W's  cancel  out, 

t  =  91  seconds. 

Again,  an  electric  car  weighing  12  tons,  running  15  miles  an  hour, 
can  stop  in  7  seconds.  What  is  the  retarding  force? 

v  =  15  miles  hour  =  22  ft.  /sec. 

F  x  7  =  12  x  22  ton  seconds. 
32.2 

F=l.l7  tons. 

Again,  a  steamboat  weighing  20,000  tons  is  being  pulled  by  a  tug- 
boat, which  exerts,  a  force  great  enough  to  overcome  the  friction  of  the 
water  and  to  give  a  net  force  of  2  tons  besides.  What  speed  will  the  boat 
acquire  in  4  minutes,  starting  from  rest? 


v  =  0.773  ft.  /sec. 

Another  application,  which  is  important  in  studying^  steam  turbines, 
windmills,  and  aeroplanes,  is  the  case  of  a  steady  stream  of  fluid  strik- 
ing against  a  solid  surface.  For  this  purpose  we  may  write  the  equation 

F-Sx'i, 

*    ,g. 

and  W/t  is  then  the  weight  of  fluid  striking  the  surface  per  second. 

One  of  the  useful  applications  of  the  momentum  equation 
is  in  studying  a  blow,  such  as  a  bat  gives  a  ball,  or  a  collision, 
as  between  two  billiard  balls.  We  naturally  speak  of  the 
forces  acting  in  such  cases  as  "  impulses,"  and  this  explains 
why  the  product  F  x  £,  which  was  first  used  in  solving  such 
problems,  is  called  "impulse." 

PROBLEMS 

(State  the  unit  in  which  each  answer  is  expressed.) 

1.  What  is  the  momentum  of  a  180-pound  football  player  running 
at  a  speed  of  20  feet  per  second? 

2.  What  is  the  momentum  of  a  66,000-ton  ship  when  it  is  going  24 
miles  an  hour  (about  21  knots)  ? 

3.  How  fast  must  a  1000-kilogram  automobile  be  going  to  have  3000 
kilogram  seconds  of  momentum  ? 

4.  A  car  weighing  12  tons,  moving  5  feet  per  second,  is  stopped  by  a 
bumper  in  0.2  seconds.     What  is  the  average  force  of  the  blow? 


ENERGY  AND  MOMENTUM  169 

5.  An  8000-ton  ship  moving  4  miles  an  hour  is  stopped  in  2   min- 
utes.    Find  the  average  force. 

6.  A   5-pound   hammer   moving  40  feet   per   second   strikes  a  nail. 
If  the  average  resistance  of  the  wood  to  the  nail  is  1240  pounds,  what 
fraction  of  a  second  was  required  to  bring  the  hammer  to  rest? 

7.  A  fire  engine  throws  a  2-inch  stream  of  water  horizontally  against 
a  brick  wall  with  a  velocity  of  150  feet  per  second.     What  is  the  force 
exerted  on  the  wall? 

8.  A  gun  delivers  100  bullets  per  minute,  each  weighing  one  ounce, 
with  a  horizontal  velocity  of  1500  feet  per  second.     What  is  the  average 
force  exerted  by  the  gun? 

SUMMARY   OF  PRINCIPLES    IN   CHAPTER   IX 

The  law  of  energy  ("How  far?"). 
Work  =  force  x  distance. 

Wv~ 
Kinetic  energy  = 

Work  done  on  body  =  gain  of  kinetic  energy. 
Work  done  by  body  =  loss  of  kinetic  energy. 

The  conservation  of  energy :  Energy  can  never  be  manufactured 
or  destroyed,  but  only  transformed  or  directed  in  its  flow. 

The  law  of  momentum  ("How  long?"). 
Impulse  =  force  x  time. 

Wv 
Momentum  =  —  • 

9 

Impulse  given  to  body  =  gain  of  momentum. 
Impulse  given  by  body  =  loss  of  momentum. 

QUESTIONS 

1.  The  pendulum  of  a  clock  would  die  down  because  of  the  friction 
of  the  air  around  it  if  energy  were  not  continually  supplied  to  it.     How 
is  this  done  ? 

2.  Look  up  "perpetual  motion"  machines   in  an  encyclopedia  and 
try  to  see  for  yourself  why  some  of  them  cannot  work. 

3.  A  certain  rifle  was   once   described  in  the  headline  of  a   maga- 
zine advertisement  as  striking  "  a  blow  of  2038  pounds."     Farther  down 
in  the  advertisement  it  appeared  that  the  bullet  weighed  ^  of  a  pound, 
and  that  its  velocity  was  2142  feet  per  second.     What  did  the  headline 
mean  ? 


CHAPTER   X 

HEAT  — EXPANSION  AND  TRANSMISSION 

Thermometer  scales  —  linear  and  volumetric  expansion  of 
solids  —  expansion  of  liquids  —  maximum  density  of  water  — 
expansion  of  gases  —  pressure  coefficient  of  gases  —  the  gas 
thermometer  and  the  absolute  scale  —  gas  formula — hot-air 
engine  —  convection  currents  —  heat  transfer  by  convection  — 
heating  and  ventilation  systems  —  conduction  —  radiation  — 
molecular  theory. 

EXPANSION  BY  HEAT 

162.  Sources  of  heat.  Our  most  important  source  of  heat 
is  the  sun.  The  sun's  rays  give  more  heat,  the  more  nearly 
vertical  they  are.  This  explains  why  we  receive  more  heat 
at  noon  than  in  the  morning  or  evening,  and  more  heat  in 
summer  than  in  winter. 

The  interior  of  the  earth  also  is  hot.  In  mine  shafts  sunk 
into  the  earth  the  temperature  rises  about  one  degree  for 
every  hundred  feet  of  depth.  Hot  springs  and  volcanoes 
also  lead  us  to  think  that  the  inside  of  the  earth  is  hot. 

To  warm  our  houses  and  run  our  engines,  we  do  not  as 
yet  depend  directly  on  the  sun  or  on  the  heat  in  the  earth, 
but  on  the  heat  produced  in  burning  wood,  coal,  oil,  or  gas. 
The  heat  thus  obtained  comes  indirectly  from  the  sun,  having 
been  stored  as  chemical  energy  in  plants  in  past  ages. 

"We  have  already  learned  in  our  study  of  machines  and  in 
our  everyday  experience  that  friction  produces  heat.  For 
example,  in  scratching  a  match,  in  using  drills,  saws,  and 
files,  indeed,  whenever  mechanical  energy  is  apparently  lost, 
we  find  that  heat  appears. 

170 


HEAT — EXPANSION    AND    TRANSMISSION 


171 


John  Tyndall  (1820-1893)  in  his  lectures  on  "  Heat  con- 
sidered as  a  mode  of  motion  "  used  to  perform  a  striking  ex- 
periment to  show  that  friction 
produces  heat. 

Let  us  try  the  same  experiment  by 
putting  a  little  water  in  a  metal  tube 
(Fig.  144).  If  we  close  the  tube 
with  a  stopper  and  rotate  it  either  by 
hand  or  with  a  motor,  we  shall  find 
that  the  friction  between  the  rotating 
tube  and  the  wooden  clamp  will  gener- 
ate in  a  few  minutes  enough  heat  to 
boil  the  water  and  blow  the  stopper 
out. 

163.  The  thermometer.    A 

FIG.  144.  —  Boiling  water  by  friction. 

deep  cellar  seems  cold  in  sum- 
mer and  warm  in  winter,  even  though  it  remains  at  nearly 
the  same  temperature.  A  room  often  seems  hot  after  we 
have  been  out  in  the  cold,  although  it  seems  chilly  after 
we  have  been  in  it  awhile.  Our  sensations  about  the 
temperature  of  things  are  therefore  very  unreliable  and 
depend  on  our  own  condition  at  the  moment.  So  it  is 
necessary  to  have  some  kind  of  instrument  to  indicate  accu- 
rately how  hot  or  cold  things  are,  that  is,  a  thermometer.  The 
usual  form  of  thermometer  is  based  on  the  fact  that  most 
liquids,  such  as  mercury  and  alcohol,  expand  when  being 
heated  and  contract  again  on  cooling. 

164.  Making   a    mercury   thermometer.     A    spherical    or 
cylindrical  bulb  is  blown  on  one  end  of  a  piece  of  glass  tub- 
ing with  a  very  fine  uniform  bore,  and  the  bulb  and  part  of 
the  stem  are  filled  with  mercury.     When  the  mercury  is 
warmed,  it  expands  and  rises  in  the  stem  until  it  overflows. 
Then  the  top  of  the  tube  is  closed  by  melting  the  glass. 
When  the  mercury  cools  again,  it  leaves  a  vacuum  in  the  top 
of  the  tube.     If  the  bulb  is  now  placed  in  the  steam  from 
boiling  water,  the  mercury  rises  to  a  definite  point  on  the 


172 


PRACTICAL  PHYSICS 


100- 


•-212- 


stem,  which  is  marked  with  a  scratch.  This  point  is  called 
the  boiling  point.  If  the  thermometer  is  then  put  in  melting 
ice,  the  mercury  goes  back  down  the  stem  and  stops  at  a 
definite  point.  This  point  is  called  the  freezing  point. 

In  thermometers  that  are  used  for  scientific  work  the 
distance  on  the  stem  between  these  two  fixed  points  is  di- 
vided into  100  equal  spaces,  called  degrees. 
In  this  thermometer,  which  is  called  a  Centi- 
grade thermometer,  the  freezing  point  is  marked 
zero  and  the  boiling  point  is  marked  one  hun- 
dred. When  these  divisions  extend  below  the 
zero  point,  they  are  called  degrees  below  zero 
or  minus  degrees. 

165.  Centigrade  and  Fahrenheit  scales.  In 
England  and  in  North  America  a  scale  de- 
vised by  Fahrenheit  is  in  common  use.  On 
this  scale  the  freezing  point  is  marked  32  de- 
grees (32°)  and  the  boiling  point  212°,  so 
that  the  space  between  the  freezing  and  boil- 
ing points  is  divided  into  180  divisions  (Fig. 
145).  Since  100  divisions  on  the  Centigrade 
scale  are  equivalent  to  180  divisions  on  the 
Fahrenheit  scale,  one  division  Centigrade  is 
equivalent  to  -|  divisions  Fahrenheit.  To 
change  a  temperature  expressed  on  the  Cen- 
tigrade scale  to  the  Fahrenheit  scale,  we  have 

FIG.  145.— Centi-    only  to  multiply  by  -|  and  add  32°.     For  ex- 
grade  and  Fah-    ample  :  — 
renheit  scales. 

30°  C  =  (f  x  30)  -f  32  =  86°  F. 

To  change  a  temperature  expressed  on  the  Fahrenheit  scale 
to  the  Centigrade  scale,  we  must  first  subtract  32°  and  then 
multiply  by  |.  For  example  :  — 

98.6°  F  =  (98.6  -  32)f  =  37°  C. 


-17.8 


\32( 


HEAT— EXPANSION    AND    TRANSMISSION 


173 


FIG.  146.  —  Minimum  and  maximum  thermometers. 


Inasmuch  as  mercury  freezes  at  —39°  C,  the  thermometers 
used  for  very  low  temperatures  contain  alcohol,  which  is 
usually  colored  red  or  blue. 

166.  Special  thermometers.  In  Weather  Bureau  stations 
the  lowest  temperature  during  the  night  and  the  highest 
temperature  during 
the  day  are  auto- 
matically recorded 
by  special  thermom- 
eters called  mini- 
mum and  maximum 
thermometers.  These  are  usually  mounted  as  shown  in  figure 
146.  The  upper  one  is  the  minimum  and  the  lower  the  maxi- 
mum thermometer.  In  the  maximum  thermometer,  the  bore 
is  constricted  just  above  the  bulb,  so  that  the  mercury  passes 
through  with  some  difficulty  when  the  tempera- 
ture rises  and  does  not  run  back  again  when  the 
temperature  falls.  The  minimum  thermometer 
is  filled  with  alcohol,  and  contains  within  its 
tube  a  small  black  index  rod,  which  is  shaped 
like  a  double-headed  pin.  As  the  temperature 
falls,  the  index  is  drawn  down  toward  the  bulb 
by  the  surface  of  the  alcohol,  and  when  the  tem- 
perature rises,  the  index  is  left  behind. 

Another  kind  of  thermometer,  which  is  used 
by  doctors  and  nurses  to  detect  fever,  is  the  clin- 
ical thermometer  (Fig..  147).  This  is  a  maxi- 
mum thermometer  on  the  Fahrenheit  scale,  and 
the  range  is  from  92°  F  to  110°  F,  each  degree 
being  divided  into  fifths.  The  normal  tempera- 
ture of  the  human  body  is  98.6°  F  or  37°  C. 


FIG.  147. 
Clinical  ther- 
mometer. 


QUESTIONS  AND  PROBLEMS 

1.  Change  to  Centigrade  :  70°  F,  150°  F,  0°F,  -10°F. 

2.  Change  to   Fahrenheit:     15°  C,    500°  C,    -26°  C, 
-  190°  C. 


174  PRACTICAL  PHYSICS 

3.  What  would  a  rise  in  temperature  of  80°  on  the  Centigrade  scale 
be  in  Fahrenheit  divisions? 

4.  The  temperature  of  the  air  on  a  certain  day  was  90°  F  at  noon  and 
45°  F  late  the  next  night.    What  was  the  "  drop  "  in  Centigrade  degrees? 

5.  At  what  temperature  do  a  Centigrade  and   a  Fahrenheit  ther- 
mometer read  the  same  ? 

6.  How  do  primitive  people  start  a  fire  ? 

7.  Why  do  sparks  fly  from  car  wheels  when  the  brakes  are  quickly 
applied  ? 

8.  Why  must  a  tool  be  kept  wet  with  cold  water  when  being  sharp- 
ened on  a  grindstone  ? 

9.  After  violent  physical  exercise  one  feels  very  hot .     Is  the  body 
temperature  higher  than  normal? 

10.  If  one  wants  the  division  marks  far  apart  on  the  stem  of  a  ther- 
mometer, what  must  be  the  relative  size  of  bulb  and  stem  ? 

167.  Expansion  by  heat  —  Solids.  When  a  railroad  track 
is  built,  a  gap  is  usually  left  between  the  ends  of  the  rails,  to 
allow  for  the  expansion  of  the  steel  in  summer.  Iron  rims 
are  placed  on  wheels  while  hot,  because  they  are  then  bigger 
and  can  be  easily  slipped  on.  When  they  cool,  they 


Fig.  148.  —  Force  exerted  by  expansion  and  contraction  of  metal  bar. 

contract  and  hold  fast  to  the  wheel.  An  ordinary  wall 
clock  loses  time  in  summer  because  its  pendulum  expands  a 
little,  and  so  swings  more  slowly.  Almost  all  solids  expand 
more  or  less  when  heated,  but  this  expansion  is  so  very 
small  that  one  must  take  special  pains  to  see  it. 

When  solids  expand  and  contract,  they  may  exert  enor- 
mous forces.  We  can  show  in  a  striking  way  the  power 
exerted  by  the  expanding  and  contracting  of  a  metal  bar  in 
the  following  experiment. 

First,  let  us  show  that  a  metal  bar  does  expand  when  heated.  In  the 
apparatus  shown  in  figure  148,  there  is  a  metal  bar  which  is  heated  by  a 


HEAT— EXPANSION    AND    TRANSMISSION          175 

series  of  little  flames  below.  The  expansion,  although  very  slight,  is 
shown  by  the  bent  lever  at  the  end,  so  that  as  the  bar  gets  hot,  the 
pointer  rises.  Second,  let  us  show  the  great  force  exerted  by  this  process. 
If  we  put  a  steel  rod  in  the  slot  at  right  angles  to  the  bar  near  the  lever, 
when  we  heat  the  metal  bar,  the  steel  rod  suddenly  breaks  and  the  pointer 
is  thrown  violently  up.  If  we  put  another  steel  rod  through  a  hole  in 
the  bar,  and  allow  the  bar  to  contract,  the  steel  rod  suddenly  snaps  and 
the  pointer  is  thrown  violently  down. 

Careful  experiments  show  that  different  metals  expand  at 
different  rates.  Platinum,  for  example,  expands  less  and 
zinc  more  than  other  common  metals.  If  we  made  a  platinum 
meter  rod  correct  at  0°C,  it  would  be  0.9  millimeters  too 
long  at  100°  C.  Similarly  a  steel  meter  rod  would  be  1.3 
millimeters  too  long,  and  a  zinc  meter  rod  would  be  2.9 
millimeters  too  long.  If  two  different  metal  strips,  such 
as  iron  and  brass,  are  riveted  together 
(Fig.  149),  forming  a  compound  bar,  the 
bar  when  heated  will  bend  or  curl,  because 
of  the  unequal  expansion  of  the  metals.  ^G  149. —  Effect  *of 
Which  metal  will  be  on  the  inner  side  heating  a  compound 
of  the  arc?  Such  compound  bars  are 
often  used  to  regulate  the  temperature  of  chicken  incubators. 

168.  Measurement  of  expansion.  In  considering  how  much 
a  given  object  —  such  as  a  steel  rail  —  will  expand,  it  is 
necessary  to  know  three  things  about  it,  namely,  its  length, 
and  the  rise  in  temperature  and  the  rate  of  expansion  of  the 
particular  substance  used.  For  example,  if  we  know  that  a 
steel  rail  is  33  feet  long  and  each  foot  of  it  expands  0.000013 
feet  per  degree  Centigrade,  we  can  compute  how  much  it 
will  expand  from  winter  to  summer,  a  range  of  perhaps 
50°  C.  The  expansion  is  equal  to  the  expansion  per  degree 
for  one  foot,  multiplied  by  the  length  in  feet  and  by  the 
rise  in  temperature.  That  is, 

Expansion  =  0.000013  x  33  x  50 

=  0.0214  feet  =  0.257  inches. 


176  PRACTICAL  PHYSICS 

We  can  express  this  in  the  form  of  an  equation,  thus, 


where       e  =  expansion, 

k  =  expansion  per  degree,  per  unit  length, 

I  =  length, 

t'  =  temperature  when  hot, 

t  =  temperature  when  cold. 

The  factor  k  is  called  the  coefficient  of  linear  expansion.  It  is 
a  very  small  fraction,  and  it  varies  with  different  substances. 
It  should  be  remembered  that  no  matter  in  what  unit  I  is 
expressed,  e  will  come  out  in  the  same  unit.  Usually  k  is 
given  per  degree  Centigrade,  but  the  coefficient  for  the 
Fahrenheit  scale  can  be  computed  by  multiplying  by  -|. 
Why? 

The  coefficients  per  degree  Centigrade  of  some  common 
substances  are  given  in  the  following  table  :  — 


Zinc 

0.000029 

Steel 

0.000013 

Lead 

0.000029 

Cast  iron 

0.000011 

Aluminum 

0.000023 

Platinum 

0.000009 

Tin 

0.000022 

Glass 

0.000009 

Silver 

0.000019 

"Invar"  (nickel 

Brass 

0.000018 

steel) 

0.0000009 

Copper 

0.000017 

169.  Some  illustrations.  In  the  .construction  of  a  steel 
bridge  allowance  has  to  be  made  for  the  expansion  of  the 
steel.  For  example,  in  the  great  bridge  over  the  Firth  of 
Forth  in  Scotland,  which  is  over  a  mile  and  a  half  long, 
the  total  expansion  amounts  to  6  feet.  In  steam  plants, 
long  pipes  are  provided  with  sliding  or  "  expansion  "  joints, 
unless  the  bends  in  the  pipe  are  such  as  to  yield  enough  for 
the  expansion. 

When  a  lamp  chimney  is  hot,  the  glass  expands.     If  a 


HEAT  — EXPANSION  AND   TRANSMISSION 


111 


drop  of  water  strikes  it,  the  glass  in  the  immediate  vicinity 
cools  rapidly  and  pulls  away  from  the  rest,  cracking  the 
chimney. 

Quartz  is  made  into  crucibles  and  other  ob- 
jects that  are  as  clear  as  glass,  but  have  so  small 
a  coefficient  of  expansion  (0.0000005)  that  a 
red-hot  crucible  may  be  suddenly  thrust  into 
water  without  cracking. 

The  pendulum  rod  of  a  clock  is  often  made 
of  dry  wood,  which  expands  very  little.  It  is, 
however,  affected  by  moisture ;  so  for  the  most 
accurate  clocks  some  kind  of  a  compensated  me- 
tallic pendulum  is  used.  One  form  of  compen- 
sated pendulum  is  that  commonly  seen  in  the 
so-called  French  clocks.  It  consists  of  a  glass 
tube  or  tubes  filled  with  mercury  (Fig.  150), 
suspended  by  a  steel  rod.  When  properly  ad- 
justed, the  raising  of  the  center  of  gravity  of  the 
mercury,  due  to  its  expansion,  is  equal  to  the 
lowering  of  the  whole  reservoir  of  mercury  due 
to  the  expansion  of  the  steel  rod,  so  that  the  ef-  FIO.  150.— Com- 
fective  length  of  the  pendulum  remains  constant,  pensated  mer- 

In  a  watch,  the  balance  wheel  if  uncompen-  ™^[  peD 
sated  will  run  slower  in  hot  weather  because 
the  hairspring  has  less  elasticity  at  a  higher  temperature,  and 
also  because  the  expansion  of  the  radius  of  the 
wheel  carries  the  rim  farther  from  the  center, 
and  so  slows  dow,n  its  rotation.  The  rim  is 
therefore  made  of  two  strips  of  metal,  brass 
on  the  outer  edge  and  steel  on  the  inner, 
fastened  with  screws  as  shown  in  figure  151. 
FIG.  151.  — Balance  When  the  temperature  rises,  the  free  ends 
wheel  of  a  watch.  o£  |-ne  rjm  curi  inward,  thus  bringing  part 
of  the  rim  nearer  the  axis.  This  compensates  for  the  expan- 
sion of  the  crossbar  and  the  weakening  of  the  hairspring. 


178  PRACTICAL  PHYSICS 

PROBLEMS 

1.  A  brass  meter  bar  is  correct  at  15°  C.     What  will  be  the  error  ai 
20°  C? 

2.  A  steel  rail  30  feet  long  is  found  to  expand  0.235  inches  when 
heated  from  -17°  F  to  100°  F.     What  is  the  coefficient  of  linear  expan- 
sion on  the  Fahrenheit  scale,  and  also  on  the  Centigrade  scale? 

3.  The  steel  cables  of  a  suspension  bridge  are  2000  feet  long.     How 
much  do  they  change  in  length  between  the  temperatures  —20°  F  and 
97°  F? 

4.  A  steel  shaft  is  heated  to  65°  C  while  being  shaped  in  a  lathe,  and 
its  diameter  at  that  temperature  is  made  just  5  centimeters.     What  will 
its  diameter  be  at  room  temperature  (15°  C)  ? 

5.  A  steel  wire,  150  centimeters  long  at  15°  C,  becomes  151.3  centi- 
meters long  when  an  electric  current  is  sent  through  it.     How  hot  does 
it  get  ? 

170.  Cubical  expansion  of  solids.    A  metal  bar  when  heated 
expands,  not  only  in  length,  but  also  in  breadth  and  thick- 
ness ;  in  short,  its  volume  increases.     This  expansion  in  vol- 
ume is  called  cubical  expansion.     Suppose  we  have  a  cube  1 
centimeter  on  an  edge  at  0°  C  and  raise  its  temperature  to 
1°  C;    each  edge  of   the   cube  will   become    (1  +  &)   centi- 
meters, k  being  the  coefficient  of  linear  expansion.      The 
original  volume,  1  cubic  centimeter,  will  become  (1  -f  &)3 
cubic  centimeters.     Now  (1  +  &)3  equals  1  +  3  k  -f  3  &2  +  jfc8  ; 
but  since  k  is  a  very  small  fraction,  the  value  of  3  k2  and  & 
will  be  so  small  that  they  may  be  neglected  without  appre- 
ciable  error.     The  volume   of   the  cube    is,  then,  1  -f-  3  k ; 
hence  the  volume  expansion  per  cubic  centimeter  per  degree 
is  3  k  cubic  centimeters  and  the  coefficient  of  cubical  expansion 
is  three  times  the  coefficient  of  linear  expansion. 

For  example,  the  coefficient  of  linear  expansion  of  glass  is  0.000009, 
and  the  coefficient  of  cubical  expansion  is  3  times  0.000009  or  0.000027. 
A  flask  which  held  just  a  liter  at  0°  C  would  hold  1002.7  cubic  centi- 
meters at  100°  C. 

171.  Expansion  Of  liquids.     Let  us  fill  a  small  round-bottomed 
flask  with  water  colored  with  ink  and  insert  a  stopper  with  a  glass  tube 


HEAT — EXPANSION  AND    TRANSMISSION 


179 


FIG.  152. 
Expansion 
of  a  liquid. 


and  paper  scale  (Fig.  152).  Then  let  us  put  the  flask  into  a  jar  of  ice 
water  and  mark  on  the  scale  the  position  of  the  liquid  in  the  tube.  If 
we  then  put  the  flask  into  a  basin  of  boiling  water,  we  shall 
note  at  first  a  sudden  drop  of  the  liquid  in  the  tube  (why?) 
and  then  a  rapid  rise.  Evidently  the  liquid  expands  more 
than  the  glass. 

In  general  it  is  found  that  liquids  expand  much 
more  than  solids.  For  example,  when  a  liter  of 
water  is  heated  from  0°  to  100°  C,  it  increases  in 
volume  about  40  cubic  centimeters,  whereas  a 
block  of  steel  of  the  same  volume  would  expand 
only  3.9  cubic  centimeters.  Alcohol,  oils,  and 
especially  kerosene  expand  even  more  than  water. 
Liquids,  like  solids,  expand  with  almost  irresist- 
ible force  when  heated,  and  exert  enormous  pres- 
sures if  expansion  is  prevented  by  their  surround- 
ings. 

In  the  case  of  liquids  and  gases,  cubical  expansion  rather 
than  linear  is  what  is  always  measured.  Since,  however,  the 
vessel  which  contains  the  liquid  expands  as  well  as  the  liquid, 

we  observe  only  the  appar- 
ent expansion.  In  a  mer- 
cury thermometer  the  ap- 
parent expansion  is  only 
about  |  of  the  real  expan- 
sion of  the  mercury.  The 
coefficient  of  cubical  expan- 
sion of  alcohol  is  0.00104, 
of  mercury  0.000181,  and 
of  water  from  0.000053  to 
0.00059  according  to  the 
temperature. 
water.  We  have  just  seen 


1.00125 


1.00025 


5°       10°      15°     20° 
TEMPERATURES, 


FIG.  153.  —  Maximum  density  of  water. 

172.    Abnormal   behavior  of 
that  solids,  liquids,  and  gases  expand  as  a  rule  when  heated  ; 
water  does  the  same  except  near  its  freezing  point. 


180 


PRACTICAL  PHYSICS 


If  we  fill  a  tall  glass  jar  nearly  full  of  cracked  ice  (Fig.  153)  and  let 
it  stand  for  a  while,  the  temperature  of  the  water  near  the  top  comes  to 
0°  C  and  remains  so,  while  the  temperature  at  the  bottom  will  be  about  4° 
C.  Since  the  heaviest  liquid  stays  at  the  bottom,  this  means  that  water 
at  4°  C  is  denser  than  water  at  0°. 

Very  precise  measurements  show  that  water  is  most  dense 
at  4°  C.  When  water  at  4°  0  is  either  warmed  or  cooled,  it 
expands  and  becomes  lighter,  as  shown  by  the  curve  in  figure  153. 
This  fact  has  many  important  conse- 
quences. For  example,  if  it  were  not  for  this, 
the  water  in  lakes  would  freeze  in  winter,  not 
merely  at  the  surface,  but  solidly  from  top 
to  bottom,  thus  destroying  all  aquatic  life. 


173.    Expansion   of   gases.    We  may  easily 
show  the  great  expansion   of  a  gas  when  heated, 
with   the   apparatus   shown   in  figure   154.     Even 
the   heat   of  the   hand  on   the  flask   causes   bub- 
bles of  air  to  be  expelled  from  the  tube  and  to 
FIG.    154.  —  Ex  pan-     rise  through  the  water.     If  the  heat  of  a  flame 
sion  of  gas.  js    applied    to    the   flask,    the    bubbles    rise    rap- 

idly. If  after  a  time  the  flame  is  removed  and  the  flask  allowed  to 
cool,  water  rises  into  the  flask  to  take  the  place  of 
the  escaped  air.  From  the  volume  of  water  thus 
drawn  up  into  the  flask,  it  is  evident  that  a  considera- 
ble fraction  of  the  air  was  expelled  during  the  expan- 
sion. 


100  c 


The  expansion  of  gases,  such  as  air,  illumi- 
nating gas,  or  acetylene,  is  remarkable  for  two 
reasons:  first,  because  it  is  so  large  —  being 
about  nine  times  as  much  as  for  water,  and 
second,  because  it  is  nearly  the  same  for  all 


o°c 


The  coefficient  of  expansion  of  a  gas  can  be  meas-  " 

*    _.                                                         ,                     j_     i            £           •  .c  J;  IG«    J.OO.  — 

ured  as  follows.     Suppose  we  have  a  tube  or  umtorm  sion  of  a  gag  un_ 

bore  (Fig.  155),  which  is  closed  at  one  end  and  has  der  constant  pres- 

a  little  pellet  of  mercury  to  separate  the  inclosed  gas  sure. 


HEAT — EXPANSION  AND    TRANSMISSION 


181 


from  the  atmosphere.  (Dry  air  is  a  good  gas  to  experiment  with.)  li 
we  put  the  tube  in  a  freezing  mixture  at  0°  C,  the  gas  in  the  tube  will 
contract,  and  we  can  measure  the  length,  which  we  will  suppose  is 
273  millimeters.  If  we  put  the  tube  in  steam  at  100°  C,  the  gas  will 
expand,  and  we  can  measure  the  length  again.  We  shall  find  that  it  is 
about  373  millimeters.  From  this  it  is  evident  that  the  gas  has  ex- 
panded 1  millimeter  for  each  degree  rise  in  temperature  (the  expansion  of 
the  glass  can  be  neglected).  That  is,  it  has  expanded  ^  or  0.00366 
of  its  volume  at  0°  C  for  each  degree  rise  in  temperature. 


study 
found 


Gay-Lussac  (1778-1850)  was  one  of  the  first  to 
the  expansion  of  gases  under  constant  pressure.  He 
that  different  gases  have  nearly  the 
same  coefficients  of  expansion,  namely 
2 {3  or  0.00366. 

174.  Pressure  coefficient  of  gases. 
Since  the  volume  of  a  gas  increases 
as  the  temperature  rises,  it  is  reason- 
able to  expect  that  if  a  certain  quan- 
tity of  gas  were  heated  and  yet  con- 
fined in  the  same  space,  the  pressure 
would  increase.  The  following  ex- 
periment shows  that  this  is  true. 


Let  us  start  with  a  gas  like  dry  air,  con- 
fined in  a  bulb  C,  which  is  connected  with 
an  open  manometer  AB,  as  shown  in  figure 
156.  At  first  we  will  surround  the  bulb  by 
melting  ice,  so  that  the  gas  is  at  0°  C,  and 
have  the  mercury  at  the  same  level  in  each 
arm  of  the  manometer,  so  that  the  gas  is 
at  atmospheric  pressure.  Then  we  will 
surround  the  bulb  with  boiling  water  at 
100°  C,  and  keep  the  gas  from  expanding 
by  pouring  mercury  into  the  manometer 
arm  B,  thus  increasing  the  pressure.  This 
increase  of  pressure  is  measured  by  the  difference  in  levels  B'  and  A. 
From  this  we  may  calculate  the  increase  per  degree  rise  in  temperature, 
and  finally  what  fraction  it  is  of  the  pressure  at  0°  C.  The  result  is 
called  the  pressure  coefficient  of  the  gas. 


FIG.  156.  —  Pressure  of  gas, 
heated  at  fixed    volume,   in- 


182  PRACTICAL   PHYSICS 

Very  careful  experiments  of  this  sort  were  first  carried 
out  by  a  Frenchman,  Regnault  (1810-1878),  who  found  that 
the  pressure  of  a  gas  kept  at  constant  volume  increases  for  each 
degree  very  nearly  ^yg-  or  0.00366  of  the  pressure  at  0°,  no 
matter  what  the  gas  is.  It  will  be  noticed  that  this  is  the 
same  fraction  which  we  found  for  the  increase  of  volume. 

To  sum  up  — 

I.    Different  gases  have  nearly  the  same  coefficients  of  ex- 
pansion; 

II.    Different  gases    have  nearly  the  same  pressure  coeffi- 
cients; 

III.  The  pressure  coefficient  of  any  gas  is  numerically  about 
the  same  as  its  coefficient  of  expansion;  each  is  about  ^y^  or 
0.00366. 

175.  Gas  thermometers.     It  is  evident  that  by  measuring 
the  increase  of  volume  of  a  gas  under  constant  pressure  or 
the  increase  of  pressure  of  a  gas  kept  at  constant  volume, 
we  have  a  means  of  measuring  temperature  changes.     Such 
a  thermometer,  filled  with   hydrogen,  is  used  as  the  world's 
standard  thermometer  at  the  International  Bureau  of  Weights 
and  Measures  near  Paris.     Since  the  hydrogen  thermometer 
has  been  chosen  as  the  standard,  it  is  important  to  know 
just  how  closely  a  good  mercury  thermometer  agrees  with  it. 
Of  course  they  agree  exactly  at  the  two  fixed  points  0°  and 
100°  C,  and  a  careful  comparison  shows  that  between  0°  and 
100°  the  difference  is  not  over  0.12°  at  any  point. 

176.  Absolute  temperature  scale.      In  the  experiment  de- 
scribed in  section  178,  we  started  with  an  air  column  273 
millimeters  in  length  at  0°  C;  if  we  had  cooled  the  gas  from 
0°  to   —  1°  C,  the  length  AB  would  have  been  shortened  a 
millimeter,  and  if  we  had  cooled  it  to  — 10°  C,  the  length  of 
the  air  column  would  have  become  263  millimeters.     If,  then, 
the  air  column  continued  to  contract  at  the  same  rate  if  cooled 
indefinitely,  the  volume  of  the  air  at  —  273°  C  would  be  zero. 


HEAT — EXPANSION  AND    TRANSMISSION 


183 


As  a  matter  of  fact,  we  can  never  get  a  gas  to  so  low  a  tem- 
perature as  —  273°  C,  for  every  known  gas,  before  that 
temperature  is  reached,  becomes  a  liquid.  This  temperature 
-  273°  C  is,  however,  one  of  unusual  interest  in  the  study  of 
gases.  It  is  called  the  absolute  zero,  and  temperatures  meas- 
ured from  this  point  as  zero  are  called  absolute  temperatures. 
Absolute  temperatures  may  be  designated  by  the  letter  A. 
Thus,  0°  C  is  273°  A,  50°  C  is  323° 
A,  and  100°  C  is  373°  A.  To 
change  any  temperature  from  the 
Centigrade  to  the  absolute  scale, 
we  have  merely  to  add  273  de- 
grees (Fig.  157). 

From    the  above    discussion  of 
absolute    temperature    it    will    be 


100s 


Cent.    Absolute 
Scale       Scale 


—  273- 


-T—  37 3*  water  boils 


— 273  ice  melts 


absolute  zero 


seen  that  the  volume  of  any  gas  FIG-  157.  —  Absolute  and  Centi- 
is  doubled  when  its  temperature  grade  scales, 

is  raised  from  273°  A  (0°  C)  to  2  x  273°,  or  546°  A  (273°  C). 
In  general,  the  volume  of  a  gas  is  very  nearly  proportional  to  its 
absolute  temperature  when  the  pressure  is  kept  constant. 

Now  since,  by  section  174,  the  coefficient  of  expansion  of 
a  gas  at  constant  pressure  is  the  same  as  the  pressure  coeffi- 
cient at  constant  volume,  when  the  volume  is  kept  constant,  the 
pressure  of  a  gas  is  proportional  to  the  absolute  temperature. 

177.  Gas  formula.  The  relation  between  the  volume  arid 
the  temperature  of  a  gas  can  be  very  concisely  expressed 
algebraically,  thus, 


V_=T_ 

v   T' 


(i) 


where    V  and  V  represent  the  .volumes  of  a  certain  gas  at 
the  same  pressure,  but  at  different  absolute  temperatures  T 
to  T' '.     If  t  is  the  temperature  on  the  Centigrade  scale  when 
the  volume  is  V,  then  T=  273  +  t ;  similarly  T'  =  273  +  t' . 
The  relation  between  the  volume  and  pressure  of  a  gas  at 


184  PRACTICAL   PHYSICS 

constant  temperature  may  be  concisely  expressed  by  Boyle's 
law  (see  section  87), 

PV=P'V,  (II) 

where  J^is  the  volume  of  a  given  quantity  of  gas  under  a 
pressure  P,  and  V1  is  the  volume  of  the  same  gas  under  a 
pressure  P1 ',  the  temperature  in  the  two  cases  being  the  same. 
The  relation  of  the  volume  to  both  pressure  and  tempera- 
ture can  be  expressed  by  the  equation, 

(Ill) 

for  it  is  readily  seen  that  this  equation  reduces  to  equation 
(II),  if  T=Tr,  and  that  if  P=P',  the  equation  becomes 
Y/T=  V /T1 ,  which  is  another  form  of  equation  (I).  Equa- 
tion (III)  is  called  the  gas  formula. 

A  problem  will  make  clear  the  use  of  the  gas  formula.  Suppose  we 
wish  to  find  the  volume  of  a  certain  quantity  of  gas  under  standard  con- 
ditions, that  is,  at  0°  C,  and  760  millimeters  pressure,  when  it  is  known 
to  occupy  120  cubic  centimeters  at  15°  C  and  under  a  pressure  of  740 
millimeters.  Substituting  in  equation  (III),  we  have 

120  x  740       V  x  760 


273  +  15    ~~   273  +  0  ' 
whence 

V  =  111  cubic  centimeters. 


PROBLEMS 

1.  At  what  temperature  on  the  Centigrade  scale  will  a  liter  of  air  at 
0°  expand  to  occiipy  2  liters,  the  pressure  being  held  constant  ? 

2.  A  certain  quantity  of  gas  occupies  350  cubic  centimeters  at  27°  C. 
What  will  be  its  volume  at  0°  C,  the  pressure  being  held  constant? 

3.  A"  steel  tank  full  of  air  at  15°  C  under  atmospheric  pressure  was 
sealed  and  thrust  into  a  furnace,  where  it  was  heated  to  1000°  C.     How 
many  atmospheres  of   pressure  did  the  air  then  exert?    Neglect   the 
thermal  expansion  of  the  steel. 

4.  A  liter  of  air  at  0°C  and  atmospheric  pressure  weighs  1.293  grams. 
What  is  the  density  of  air  at  100°  C  and  atmospheric  pressure  ? 


HEAT— EXPANSION    AND    TRANSMISSION 


185 


5.  A  student  in  a  chemical  laboratory  generates  50  liters  of  hydrogen 
at  10°  C,  and  at  a  pressure  of  700  millimeters.     Find  the  volume  of  the 
gas  under  standard  conditions;  that  is,  at  0°  C  and  at  760  millimeters. 

6.  At   the  beginning  of  the  so-called  "  compression  stroke "  in  an 
automobile  engine,  its  cylinder  contains  42  cubic  inches  of  gas  and  air  at 
atmospheric  pressure,  and  at  a  temperature  of  40°  C.     At  the  end  of  the 
compression  the  volume  is  6  cubic  inches  and  the  pressure  is  15  atmos- 
pheres.    What  is  the  temperature  ? 

178.  Low  temperatures.     The  investigations  of  Lord  Kel- 
vin (1824-1907)  and  of  other  scientific  men  all  point  to  the 
conclusion  that  the  temperature  —  273°  C  is  really  an  absolute 
zero  in  the  same  sense  that  it  is  the  lowest  possible  temperature 
in  the  universe.      Although   no  one  has  as  yet  succeeded  in 
cooling  a  body  to  absolute  zero,  temperatures  within  a  very 
few  degrees  of  this  point  have  been  attained  by  the  evapora- 
tion of  liquefied  gases.     With  liquid  air,  temperatures  as  low 
as   —  200°  C  may  be  obtained,    and    with   liquid  hydrogen 

-  258°  C.  In  1908  Professor  Chines,  at  the  University  of 
Leyden  in  Holland,  found  that  the  boiling 
point  of  liquid  helium  is  —  268.6°  C,  or  only 
about  4.5°  above  the  absolute  zero,  and  he 
has  since  cooled  liquid  helium  to  within  2° 
of  the  absolute  zero.  At  these  low  temper- 
atures rubber  and  steel  become  as  brittle  as 
glass,  and  metals  become  much  better  con- 
ductors of  electricity  than  at  ordinary  tem- 
peratures. 

179.  Hot-air  engine.     An  interesting  ap- 
plication of  the  expansion  of  gases  is  the 
hot-air  engine.      Its  operation  can  be  best 
understood    by    studying    figure  158.      A 
loosely  fitting   plunger   A  moves  up  and 
down   and  thus    shifts   the   air    back   and 
forth  in  the  cylinder  (7,  which  is  heated  at 

the  bottom  and  kept  cool  at  the  top.     The  working  cylinder 
Of  has  a  nicely  fitting  piston  $. 


FIG.   158. —  Diagram 
of  hot-air  engine. 


186 


PRACTICAL   PHYSICS 


When  the  plunger  A  moves  down,  the  hot  air  below  is 
transferred  to  the  top,  where  it  is  cooled.  This  makes  it  con- 
tract. The  piston  13  is  then  forced  down 
by  the  external  pressure  of  the  atmosphere. 
As  soon  as  the  piston  B  is  near  the  bottom 
of  its  stroke,  the  plunger  A  is  raised,  caus- 
ing the  air  to  flow  back  under  A,  where  it 
is  heated  by  the  fire.  This  makes  it  ex- 
pand and  forces  the  piston  B  up  again,  and 
so  the  cycle  is  repeated. 

These  engines  are  commonly  used  for 
pumping  water  on  a  small  scale  at  isolated 
places,  for  they  do  not  require  expert  at- 
tendants, and  they  use  any  kind  of  fuel. 
In  general  they  cannot  compete  with  gas 
engines  on  account  of  their  bulk  and  the 
rapid  wearing  out  of  the  heating  surfaces. 
180.  Convection  currents.  All  systems 
of  heating  and  ventilation  depend  upon 
what  are  called  convection  currents, 
which  in  turn  depend  upon  the  expan- 
sion of  liquids  and  gases.  To  make  these 
clear,  let  us  try  two  simple  experiments. 

We  cut  off  the  bottom  of  a  bottle  and 
bend  a  glass  tube  (Fig.  159)  so  that  the 
ends  can  be  slipped  through  a  stopper 
which  fits  the  neck  of  the  bottle.  If  we 
invert  the  bottle  and  fill  it  with  water 
containing  a  little  sawdust,  we  can  see  a 
circulation  of  the  water  when  a  flame  is 
waved  back  and  forth  from  A  to  B.  We 
note  that  the  direction  is  from  A  to  B. 
Why? 

A  box  (Fig.  160)  has  a  glass  front,  and 
two  holes  in  the  top,  which  are  covered 
with  glass  chimneys.     If  we  put  a  candle    FlG>  m  _  Convection  current 
under  one  chimney,  convection  currents  of  air. 


FIG.  159.  —Convection 
current  of  water. 


HEAT — EXPANSION    AND    TRANSMISSION 


187 


of  air  go  down  the  cool  chimney  and  up  the  warm  one.  A.  bit  of  lighted 
touch  paper  held  near  the  top  of  the  cool  chimney  makes  the  convection 
currents  more  evident. 

The  draft  in  a  lamp,  stove,  fireplace,  or  power-house 
chimney  is  a  convection  current* 

The  explanation  of  the  movement  of  convection  currents 
is  that  any  gas  or  liquid  expands  when  heated,  so  that  a 
given  quantity  of  fluid  increases  in  volume  and  consequently 
decreases  in  density.  In  a  convection  current,  the  lighter 
fluid  is  pushed  up  by  the  heavier  surrounding  fluid,  just  as 
a  block  of  wood  under  water  is  pushed  up  by  the  surround- 
ing water. 


TRANSMISSION  OF  HEAT 

181.  Heat  transfer   by   convection. 
Since  the  up-going  part  of  a  convec- 
tion current  is  warmer  than  the  re- 
turning  part,  there  is  a  transfer  of 
heat  from  the  flame  or  other  source 
of  heat  at  the  bottom,  to  the  cooler 
parts  of  the  circuit  at  the  top.     This 
process  of  transporting  heat  by  carry- 
ing hot  bodies  or  hot  portions  of  a  fluid 
from  one  place  to  another  is  called  con- 
vection.    It  is  the  basis  of  almost  all 
systems  for  heating  buildings. 

182.  Hot-water  heating.       The  ar- 
rangement   for    heating   water    in    the 

kitchen  range  for  general  use  in  laundry  FlG- 161  -Hot-water  heater, 
and  bathroom  is  shown  in  figure  161.  The  cold  water  en- 
ters the  tank  through  a  pipe  which  reaches  nearly  to  the  bottom. 
From  the  bottom  of  the  tank  the  water  is  led  to  a  heating 
coil  along  the  side  of  the  fire  box  in  the  range.  When  the 
water  becomes  hot,  it  is  pushed  up  and  goes  back  into  the 


188 


PRACTICAL  PHYSICS 


tank  at  a  point  nearer  the  top.  Thus  a  circulation  is  set  up 
which  continues  until  practically  all  the  water  in  the  tank 
has  passed  through  the  stove  and  the  whole  tankful  is  hot. 
The  hot-water  system  of  heating  houses  depends  on  this  same 
principle  of  convection.  Water  is  heated  nearly  to  the  boil- 
ing point  in  a  furnace  in  the  basement.  The  hot  water  is 
led  from  the  top  of  the  furnace  through  pipes  to  iron  radia- 
tors in  the  various  rooms  of  the  building.  On  account  of 
the  large  exposed  surface  in  each  radiator,  heat  is  rapidly 
given  out  by  the  hot  water  to  the  surrounding  air.  The 

cooled  water  is  then  carried 
from  the  radiators  through 
return  pipes  to  the  base  of 
the  furnace.  To  prevent  ra- 
diation from  the  pipes,  a  thick 
non-conducting  coating  of  as- 
bestos is  often  provided. 

153.  Hot-air  system  of  heat- 
ing and  ventilating.  The  hot- 
air  furnace  in  the  basement 
(Fig*.  162)  is  simply  a  big 
stove,  surrounded  by  a  shell 
or  jacket  of  galvanized  sheet 
iron.  The  air  between  the 

stove  and  outer  shell  is  heated,  and  is  then  pushed  up  into 
the  flues  by  the  heavier  cold  air  which  comes  in  from  out  of 
doors  through  the  cold-air  inlet  flue.  The  smoke,  of  course, 
goes  up  the  chimney.  The  warm  air  which  enters  the  rooms 
finds  an  outlet  around  the  doors  and  windows. 

In  the  hot-water  system  of  heating  there  is  no  provision 
whatever  for  changing  the  air  in  the  room  ;  that  is,  for  venti- 
lation. In  the  hot-air  system,  a  small  quantity  of  fresh  air 
is  continually  flowing  into  the  rooms.  This  is  enough  for  a 
private  house.  But  in  schools,  churches,  and  other  public 
buildings,  large  quantities  of  clean,  fresh,  warm  air  have  to 


FIG.  162.  —The  hot-air  furnace. 


HEAT— EXPANSION  AND    TRANSMISSION 


189 


be  continually  supplied  by  other  means.  For  the  proper 
ventilation  of  a  room  it  is  estimated  that  each  person  in  it 
requires  about  50  cubic  feet  of  fresh  air  every  minute.  In 
large  modern  school  buildings  the  air  is  drawn  in  from  out 
of  doors  by  powerful  fans,  filtered  through  cloth,  warmed  by 
passing  around  steam  pipes,  and  then  distributed  in  ducts 
throughout  the  building.  The  vitiated  air  in  each  room  is 
forced  out  through  ducts  near  the  floor.  This  indirect  system 
of  heating,  while  expensive,  furnishes  excellent  ventilation. 

184.  Conduction  in  solids.  Besides  transporting  heat  from 
one  place  to  another  by  carrying  hot  bodies  about,  or  making 
hot  fluids  flow  through  pipes,  we  can  transmit  heat  from  one 
place  to  another,  without  moving  any  material  thing,  by 
either  of  two  methods  called  conduction  and  radiation. 

Every  one  knows  that  the  handle  of  a  silver  spoon  gets 
hot  when  its  bowl  is  in  a  cup  of  hot  tea  or  coffee.  If  one 
end  of  an  iron  poker  is  put  in  the  fire,  the  other  end  gets  un- 
comfortably hot  and  must  be  provided  with  a  wooden  handle. 
Yet  if  a  wooden  rod  is  plunged  into  a  fire,  it  is  hard  to  feel 
any  warmth  at  the  other  end.  So  we  conclude  that  silver 
and  iron  conduct  heat  better  than  wood.  In  general,  metals 
are  good  conductors  of  heat. 

There  are  some  substances,  such  as  stone,  glass,  wood, 
wool,  fur,  and  ashes,  which  are  poor  conductors  of  heat  and 
are  therefore  called  heat  insulators.  The  metals,  such  as  silver, 
copper,  brass,  iron,  lead,  etc.,  are  good  conductors  as  compared 
with  the  non-metals.  Careful  study  shows  that  even  the 
metals  vary  in  their  power  to  conduct  heat,  that  is,  in  con- 
ductivity. |\  V 

This  can  be  shown 
by  the  following  ex- 
periment. 

Let  us  fasten  with 
sealing  wax  a  number 
of  steel  balls  at  regular  FIG.  163.  —  Relative  conductivity  of  copper  and  iron. 


190 


PRACTICAL   PHYSICS 


intervals  on  the  under  side  of  two  rods,  one  of  copper  and  the  other  of  iron. 
If  we  heat  one  end  of  each  rod  in  a  flame  (Fig.  163),  the  balls  on  the 
copper  rod  soon  begin  to  drop  off,  beginning  near  the  flame.  Later  the 
balls  on  the  iron  rod  begin  to  drop  off.  Often  half  the  balls  will  haye 
dropped  from  the  copper  rod  before  the  first  one  drops  from  the  iron  rod. 

185.    Conduction  in  liquids  and  gases.     Liquids  and  gases 
-,  ft    are    much    poorer   conductors 
than   metals.       This   can    be 
shown    by   the    following    ex- 
periments. 


FIG.  164.  —  Water  a  non-conductor. 


Let  us  take  a  test  tube  full  of 
water  and  place  in  it  a  few  pieces 
of  ice  which  are  held  in  the  bottom 
by  a  wire,  as  shown  in  figure  164. 
Then  we  may  boil  the  water  at  the 
top  of  the  tube  for  some  time  with- 
out melting  the  ice  in  the  bottom. 

Another  more  striking  experiment  to  show  the  poor  conductivity  of 
water  is  shown  in  figure  165.  The  bulb  of  the  air  thermometer  is  placed 
only  half  an  inch  below  the  surface  of  the  water  in  the  funnel.  When 
a  spoonful  of  ether  is  poured  on  the  surface  of  the  water  and  lighted,  the 
liquid  in  the  tube  of  the  air  thermometer  will  re- 
main practically  stationary,  in  spite  of  the  fact  that 
the  air  thermometer  is  very  sensitive  to  changes  in 
temperature. 

Experiments  to  measure  conductivity 
show  that  iron  conducts  100  times  as  well 
as  water,  and  that  water  conducts  25  times 
as  well  as  air.  In  general,  it  may  be  said 
that  liquids  and  gases  are  very  poor  con- 
ductors of  heat. 

It  is  an  interesting  fact  that  substances 
which  are  good  conductors  of  heat  are 
good  conductors  of  electricity  as  well. 

186.    Applications.     These  differences  in    FIG.  165.  — Burning 
conductivity    explain    why    teapots    have       ®ther  on  tla*  water 

\         IT,         i ,  does  not  affect  the 

wooden  or  insulated  handles ;  why  steam       air  thermometer 


HEAT— EXPANSION    AND    TRANSMISSION 


191 


pipes  are  covered  with  wool,  magnesia,  or  asbestos  ;  why 
double  windows  are  used  in  cold  climates ;  why  a  vacuum 
bottle  (Fig.  166)  keeps  things  hot  or 
cold;  and  why  we  wear  woolen  clothing 
in  winter.  Woolen  clothing  of  loose 
texture,  furs  and  feathers,  or  eiderdown 
quilts  are  effective  as  heat  insulators  be- 
cause so  much  air  is  inclosed  in  their 
pores. 

Differences  in  conductivity  also  account 
for  many  of  our  curious  sensations  of  heat 
and  cold.     Thus  in  a  cool  room  some  things 
feel  much  colder  than  others.       Metallic 
objects,  which  are  good  conductors,  take    FIQ.  166.  —  Section  of 
heat  rapidly  from  the  hand,  and  so  give      vaTuTm^a^ver* 
the  sensation  of  cold.      While  other  ob-      poor  conductor  of 
jects,  such   as  wood   and   paper,   do   not      heat' 
carry  off  the  heat  of  the  hand  and  so  do  not  feel  cold.     Sim- 
ilarly a   piece  of   metal   lying   in   the  hot  sun  feels    much 
warmer  than  a  piece  of  wood  beside  it. 

187.  Radiation.  If  an  iron  ball  is  heated  and  hung  up  in 
the  room,  the  heat  can  be  felt  when  the  hand  is  held  under 
the  ball.  This  cannot  be  due  to  convection,  because  the  hot- 
air  currents  would  rise  from  the  ball.  It  cannot  be  due  to 
conduction  because  gases  are  very  poor  conductors.  Simi- 
larly a  lighted  electric  light  bulb  feels  hot  if  the  hand  is 
held  near  it,  but  when  the  light  is  turned  off,  the  sensation 
stops  very  quickly.  The  glass  of  the  bulb  is  a  very  poor 
conductor  and  there  is  practically  no  air  left  inside  the  bulb, 
so  that  the  sensation  of  heat  can  be  due  neither  to  convection 
nor  to  conduction.  Furthermore,  an  enormous  quantity  of 
heat  comes  to  us  from  the  sun.  Yet  men  who  make  ascents 
in  balloons  and  aeroplanes  find  that  the  air  becomes  less  and 
less  dense,  so  that  it  seems  reasonable  to  suppose  that  the 
earth's  atmosphere  forms  a  coating  only  a  few  miles  thick 


192  PRACTICAL   PHYSICS 

and  that  the  space  beyond  is  absolutely  empty.  So  the  sun's 
heat  cannot  come  by  convection  or  conduction. 

Scientists,  to  explain  these  phenomena,  have  imagined  a 
weightless,  elastic  fluid  called  the  ether  which  fills  all  space 
and  transmits  heat  and  light  by  a  process  called  radiation. 
When  a  body  not  in  contact  with  conducting  bodies  cools, 
it  is  said  to  radiate  heat,  or  to  cool  by  radiation.  If  one 
places  a  screen,  such  as  a  book,  -between  a  lighted  lamp  and 
his  face,  he  no  longer  feels  the  heat.  So  we  think  that  heat 
rays,  like  light  rays,  travel  in  straight  lines.  Experiments 
also  show  that  heat  rays,  like  light  rays,  can  be  reflected  by  a 
mirror,  or  brought  to  a  focus  by  a  burning  glass. 

Some  substances,  such  as  glass  and  air,  let  the  sun's  heat 
rays  pass  through  almost  unimpeded  and  are  warmed  but 
little  by  this  radiant  heat  ;  that  is,  they  are  "  transparent-to- 
heat."  Other  substances,  such  as  water,  do  not  let  heat  pass 
through  and  are  warmed  by  any  radiant  heat  rays  that 
strike  them  ;  they  are  "opaque-to-heat." 

A  mirror,  or  any  highly  polished  surface,  is  a  good  heat 
reflector,  and  yet  itself  remains  cold.  Fresh  snow  melts 
slowly  in  the  sun's  rays,  but  snow  covered  with  soot  or 
black  dirt  melts  rapidly.  In  general,  reflecting  or  white 
objects  do  not  easily  absorb  radiant  heat,  while  rough  or  black 
objects  absorb  heat  readily. 

It  has  also  been  found  that  reflecting  and  bright-colored 
objects,  when  hot,  cool  by  radiation  more  slowly  than  rough 
and  dark  objects.  For  example,  a  brightly  polished  silver 
cup  radiates  heat  twenty  times  more  slowly  than  a  sooty 
black  cup.  In  general,  good  absorbers  are  good  radiators,  and 
poor  absorbers  are  poor  radiators. 

188.  Theory  as  to  what  heat  is.  There  are  many  reasons 
for  thinking  that  heat  is  a  rapid  vibratory  motion  of  the 
molecules  of  substances  or  of  the  ether  which  fills  the  spaces 
between  the  molecules.  We  imagine  that  the  molecules  in 
a  hot  flatiron  are  vibrating  more  rapidly  than  when  it  was 


HEAT — EXPANSION    AND    TRANSMISSION          193 

cold,  and  that  this  molecular  vibration  extends  to  the  sur- 
rounding ether  and  so  is  sent  out  in  straight  lines  in  all  di- 
rections as  radiant  heat. 

At  a  temperature  of  about  550°  C  iron  becomes  "  red  hot," 
and  at  1300°  C  it  gets  "  white  hot."  We  imagine  that  the 
iron,  before  it  begins  to  glow,  is  sending  out  dark  heat  rays, 
but  that,  when  red  hot  or  white  hot,  it  is  sending  out 
visible  heat  rays,  that  is,  light  rays.  We  think  that  these 
heat  rays  and  light  rays  differ  only  in  the  rapidity  of  the 
vibratory  motion,  and  in  their  effect  on  man's  organs  of 
sense.  If  the  vibrations  are  under  400  trillion  per  second,  we 
recognize  them  as  heat;  but  if  the  vibrations  are  between  400 
and  800  trillion  per  second,  the  nerves  of  the  eye  recognize 
them  as  light.  Heat  and  light  are  both  forms  of  radiant 
energy.  This  radiant  energy  travels  at  the  enormous  speed 
of  187,000  miles  per  second,  which  means  that  radiant 
energy  could  circle  the  earth  seven  times  in  one  second. 

On  this  theory,  the  expansion  of  bodies  when  heated  is 
due  to  the  more  violent  vibration  of  their  molecules,  which 
require  more  room  to  move  about  in.  At  a  certain  tem- 
perature this  motion  becomes  so  violent  that  the  molecules 
break  away  froni  their  former  position  and  the  body  changes 
its  state  ;  that  is,  it  melts  or  boils. 


SUMMARY    OF  PRINCIPLES   IN   CHAPTER  X 

100  Centigrade  degrees  =  180  Fahrenheit  degrees. 
Temp.  Fahr.  =  (f  Temp.  Cent.)  +  32. 
Temp.  Cent.  ==  f  (Temp.  Fahr.  —  32). 

Coefficient  of  linear  expansion = expansion  per  degree  for  unit  length 

_  total  expansion 

total  length  x  rise  in  temperature 

Total  expansion  =  coefficient  x  length  x  rise  in  temperature, 
o 


194  PRACTICAL  PHYSICS 

Coefficient  of  volume  expansion 

=  expansion  per  degree  for  unit  volume, 

total  expansion 

total  volume  x  rise  in  temperature 

Total  expansion  =  coefficient  x  volume  x  rise  in  temperature. 

For  solids,  volume  coefficient  =  3  x  linear  coefficient. 

Pressure  coefficient  of  gases  = total  pressure  rise 

pressure  x  rise  in  temperature 
Total  pressure  rise  =  coefficient  x  pressure  x  rise  in  temperature, 


1 


Volume  coefficient  of  all  gases  nearly  the  same. 
Pressure  coefficient  of  all  gases  nearly  the  same.     Value 
Volume  and  pressure  coefficients  nearly  equal. 


Gas  law: 


QUESTIONS 

1.  Is  friction  ever  a  source  of  useful  heat? 

2.  Are  the  sun's  rays  ever  used  practically  as  a  direct  source  of  heat 
for  engines? 

3.  Why  does  spring  water  seem  warm  in  winter  and  cool  in  summer? 

4.  Why  does  the  water  seem  much  colder  before  a  bath  than  after- 
wards ? 

5.  Why  can  a  platinum  wire  be  sealed  or  melted  into  glass  while  a 
copper  wire  cannot  ? 

6.  Why  do  glass  bottles  crack  when  placed  on  a  hot  stove  ? 

7.  Why  do  apples  and  pieces  of  green  wood  swell  when  heated  ? 

8.  Why  is  there  a  cold  indraft  of  air  at  the  bottom  of  an  open 
window? 

9.  Is  there  any  other  reason  than  convenience  for  putting  furnaces 
in  cellars  rather  than  in  attics  ? 

10.  How  is  the  water  which  is  standing  in  the  hot-water  pipes  in  a 
house  kept  hot  ? 

11.  Does  a  hot  body  cool  more  rapidly  if  placed  on  metal  than  if 
placed  on  wood  ?    Why  ? 


HEAT  — EXPANSION  AND   TRANSMISSION  195 

12.  Why  does  a  glowing  coal  die  out  quickly  on  a  metal  shovel,  and 
yet  glow  for  a  long  time  in  ashes? 

13.  How  does  a  fire  less  cooker  work  ? 

14.  Look  up  Davy's  lamp  for  miners  in  an  encyclopedia.     What  is  its 
advantage  ?     Why  is  it  that  a  flame  will  not  strike  through  the  fine-net 
wire  gauze  ? 

15.  Why  are  the  walls  of  ice  houses  often  packed  with  sawdust? 

16.  Why  should  an  air  space  be  left  in  building  the  walls  of  brick  and 
cement  houses? 

17.  Does  woolen  ctothing  supply  any  heat  to  maintain  the  body's 
temperature  ? 

18.  Why  do  people  prefer  to  wear  white  clothes  in  summer  and  in 
hot  countries? 

19.  Why  should  the  surface  of  a  teakettle  be  brightly  polished  and 
the  bottom  blackened  ? 

20.  Is  it  advisable  to  put  any  sort  of  aluminum  or  gold  paint  on  a 
radiator  that  is  to  heat  a  room  ? 

21.  Describe  carefully  the  "dampers"  of  some  stove  or  furnace  you 
have  seen,  and  explain  how  they  accomplish  the  desired  results. 


CHAPTER   XI 
WATER,   ICE,  AND   STEAM 

Measurement  of  heat— B.  t.  u.  and  calorie  —  specific  heat  — 
freezing  point  —  change  of  volume  in  freezing  —  latent  heat, 
ice  to  water  —  boiling  point  under  various  pressures  — dis- 
tillation— latent  heat,  water  to  steam  —  humidity  —  fog,  rain, 
and  snow  —  artificial  ice. 

189.  How  we  measure  heat.  If  a  man  buys  a  ton  of  coal, 
what  does  he  get  for  his  money  ?  One  answer  would  be, 
about  2000  pounds  of  material,  of  which,  perhaps,  40  pounds 
is  water,  320  pounds  is  ash,  and  the  rest  mostly  carbon  and 
hydrogen.  What  the  man  is  really  interested  in,  however, 
is  not  the  sort  of  material,  but  the  amount  of  heat  he  has 
bought.  Since  heat  is  not  a  substance,  but  a  form  of  energy, 
we  cannot  measure  it  directly  in  pounds  or  quarts,  but  must 
measure  it  by  the  effect  it  caii  produce.  For  example,  if  one 
pound  of  hard  coal  could  be  completely  burned,  and  if  all 
the  heat  generated  in  this  process  could  be  used  to  heat 
water,  it  would  be  found  that  about  7  tons  of  water  could  be 
raised  1°  F  in  temperature.  Engineers  reckon  the  heat  value 
of  fuel  in  units  sucli  that  each  represents  the  heat  required  to 
raise  one  pound  of  water  one  degree  Fahrenheit.  This  heat 
unit  is  called  the  "  British  thermal  unit,"  and  is  written  B.  t.  u. 
For  example,  the  heat  value  of  a  pound  of  coal  varies  from 
11,000  to  16,000  B.  t.  u. ;  a  pound  of  petroleum  gives  about 
25,000  B.  t.  u.,  a  pound  of  gasolene  about  19,000  B.  t.  u.,  and 
a  pound  of  dry  wood  about  5000  B.  t.  u. 

The  heat  unit  employed  in  Europe,  and  in  all  physical  and 
chemical  laboratories,  is  a  metric  unit  called  the  calorie.  The 
calorie  is  the  heat  required  to  raise  the  temperature  of  a  gram 
of  water  one  degree  Centigrade. 

196 


WATER,   ICE,   AND   STEAM 


197 


190.  Heat  absorbed  by  different  substances.  It  is  well 
known  that  a  kettle  of  water  on  a  stove  gets  warm  much  less 
quickly  than  a  flatiron  of  the  same  weight.  For  example, 
the  heat  required  to  warm  a  kilogram  of  water  1  degree  will 
warm  the  same  weight  of  copper  10  degrees,  of  silver  or  tin 
20  degrees,  and  of  lead  or  mercury  30  degrees.  In  fact 
experiments  show  that  water  requires  more  heat  per  unit 
weight  per  degree  rise  of  temperature  than  any  other  common 
substance. 

Since  one  calorie  is  required  to  raise  the  temperature  of 
one  gram  of  water  one  degree,  only  one  tenth  of  a  calorie  would 
be  needed  to  raise  the  temperature  of  one  gram  of  copper  a 
degree,  one  twentieth  of  a  calorie  to  raise  a  gram  of  silver 
one  degree,  and  one  thirtieth  of  a  calorie  to  raise  a  gram  of 
lead  one  degree.  The  number  of  calories  required  to  raise  the 
temperature  of  a  gram  of  a  substance  one  degree  Centigrade 
is  called  its  specific  heat.  Thus  the  specific  heat  of  water  is 
1,  of  copper  about  0.1,  etc. 

The  following  experiment  of  Tyndall's  illustrates  how 
much  substances  differ  in  their  specific  heats. 

We  may  heat  a  number  of  balls  of  the  same 
weight  but  of  different  metals,  such  as  iron;  zinc, 
copper,  lead,  and  tin,  to  about  150°  C  in  oil. 
Then  if  we  place  them  all  at  the  same  time  on  a 
thin  cake  of  paraffin  wax  which  is  held  on  a  ring, 
as  shown  in  figure  167,  they  will  melt  the  wax 
and  sink  into  it,  but  at  different  rates.  The 
iron  works  its  way  most  vigorously  into  the 
wax,  and  even  through  the  cake.  The  zinc  and 
copper  balls  come  next,  while  the  lead  ball 
makes  but  little  headway.  The  metal  with 
the  largest  specific  heat,  iron,  gives  out  the 
largest  amount  of  heat  in  cooling  and  so  melts  JTIG  167  _  Metals  differ 
the  most  paraffin.  in  specific  heat. 

191  How  specific  heat  is  determined.  When  a'  hot  sub- 
stance, such  as  hot  mercury,  is  poured  into  cold  water,  the 


198  PRACTICAL   PHYSICS 

water  and  mercury  soon  come  to  the  same  temperature.  The 
heat  given  up  by  the  cooling  mercury  is  used  in  warming 
the  water.  If  no  heat  is  lost  in  the  process,  the  heat  units 
given  out  by  the  hot  body  are  equal  to  the  heat  units  gained  by 
the  cold  body. 

This  method  of  mixtures  is  accurate  only  when  no  heat  is 
lost  during  the  transfer.  This  is  rather  difficult  to  manage  in 
practice.  Nevertheless,  this  method  is  the  one  generally  used 
in  laboratories  to  determine  the  specific  heat  of  substances. 

For  example,  suppose  that  300  grams  of  mercury  are  heated  to  100°  C 
and  then  quickly  poured  into  100  grams  of  water  at  10°  C,  and  that,  after 
stirring,  the  temperature  of  the  water  and  mercury  is  18.2°  C. 

If  we  let  x  be  the  specific  heat  of  the  mercury,  the  mercury  gives  out 
300(100  -  18.2)z  calories.  Since  the  specific  heat  of  water  is  1,  the 
water  absorbs  100(18.2  —  10)1  calories.  Therefore  we  may  make  the 
equation 

300(100  -  18.2)*  =  100(18.2  -  10)1, 
whence  x  =  0.033  calories. 

By  very  careful  experiments  of  this  sort  the  specific  heats 
of  some  of  the  common  substances  have  been  found  to  be  as 

follows  :  — 

TABLE  OF  SPECIFIC  HEATS 


Water  1.00 

Pine  wood  0.65 

Alcohol  0.60 

Ice  0.50 

Aluminum  0.22 


Sand  0.19 

Iron  0.12 

Copper  0.094 

Zinc  0.093 

Mercury  0.033 


It  is  remarkable  that  of  all  ordinary  substances  water  has 
the  greatest  specific  heat.  Thus  it  takes  about  four  times  as 
much  heat  to  raise  a  pound  of  water  one  degree  as  to  raise  a 
pound  of  solid  earth  one  degree,  and  so  the  ocean  acts  as  a 
great  moderator  of  temperatures.  In  summer  the  water 
absorbs  a  vast  amount  of  heat  which  it  slowly  gives  up  in 
winter  to  the  land  and  air.  This  explains  why  the  tempera- 
ture on  some  ocean  islands  does  not  vary  more  than  10°  F 
during  the  whole  year. 


WATER,   ICE,  AND   STEAM  199 


PROBLEMS 

1.  How  many  calories  of  heat  are  needed  to  raise  the  temperature 
of  10  grams  of  water  5°  C  ? 

2.  How  many  calories  are  required  to  heat  15  grams  of  iron  20°  C  ? 

3.  Compute  the  calories  given  out  by  a  kilogram  of  copper  in  cool- 
'ngfrora  110°  C  to!5°C. 

4.  How  many  B.  t.  u.  are  necessary  to  heat  a  2-pound  flatiron  from 
70°  F  to  350°  F  ? 

5.  If  the  heat  value  of  coal  is  14,000  B.  t.  u.  per  pound,  how  many 
tons  of  water  can  be  heated  from  32°  to  212°  F  by  the  combustion  of  one 
ton  of  coal  in  a  boiler  whose  efficiency  is  75  %  ? 

6.  If  400   grams  of   water  at  100°  C  are  mixed  with  100  grams  of 
water  at  20°  C,  what  will  be  the  temperature  of  the  mixture? 

7.  It'  500  grams  of  copper  at  100°  C,  when  plunged  into  300  grams  of 
water  at  10°  C,  raise  the  temperature  to  22°  C,  what  is  the  specific  heat 
of  copper? 

8.  A  piece  of  iron  weighing  150  grams  is  warmed  1°  C.     How  many 
grams  of  water  could  be  warmed  1°  by  the  same  amount  of  heat  ?     (The 
answer  is  called  the  water  equivalent  of  the  piece  of  iron.) 

9.  A  50-pound  iron  ball  is  to  be  cooled  from  1000°  F  to  80°  F,  by 
putting  it  in  a  tank  of  water  at  32°  F.     How  many  pounds  of  water  must 
there  be  in  the  tank? 

10.  A  platinum  ball  weighing  100  grams  is  heated  in  a  furnace  for 
some  time,  and  then  dropped  into  400  grams  of  water  at  0°  C,  which  is 
raised  to  10°  C.  How  hot  was  the  furnace?  (Sp.  heat  =  0.04.) 

192.  Melting  and  freezing.  If  one  brings  in  from  out  of 
doors  on  a  cold  winter  day  a  pailful  of  snow  or  ice  and  sets 
it  on  a  stove,  he  finds  that  its  temperature  is  at  first  below 
0°  C  and  slowly  rises  to  that  point.  It  then  remains 
stationary,  or  nearly  so,  until  all  the  snow  is  melted.  Then 
the  temperature  of  the  water  gradually  rises.  This  stationary 
temperature,  where  the  ice  (snow)  changed  to  water,  is 
called  the  melting  point  of  ice,  and  is  0°  C  or  32°  F. 

We  may  also  determine  the  freezing  point  of  water  by 
making  a  freezing  mixture  of  cracked  ice  and  salt  and  placing 
in  it  a  test  tube  containing  some  pure  water.  The  tempera- 
ture of  the  water  will  be  observed  to  fall  slowly  until  the 
water  begins  to  freeze.  Then  the  temperature  remains  con- 


200 


PRACTICAL  PHYSICS 


stant  until  all  the  water  is  frozen.  This  stationary  tempera- 
ture at  which  water  changes  into  ice  is  called  the  freezing 
point  of  water,  and  is  0°  C  or  32°  F. 

Substances  which  are  crystalline,  such  as  ice  and  many 
metals,  change  into  liquids  at  a  definite  temperature,  and 
the  melting  point  of  such  a  substance  is  the  same  as  its  freez- 
ing point. 

TABLE  OF  MELTING  OR  FREEZING  POINTS 


Platinum 

Steel 

Glass 

Copper 

Gold 

Silver 

Lead 


above  1700°  C 

1300  to  1400°  C 

1000  to  1400°  C 

1083°  C 

1062°  C 

960°  C 

327°  C 


Tin  232°  C 

Sulphur  115°  C 
Naphthalene  (moth  balls)       80°  C 

Paraffin  about  54°  C 

Ice  0°  C 

Mercury  -  39°  C 

Alcohol  about  -  112°  C 


Non-crystalline  substances,  such  as  iron,  glass,  and  paraffin, 
pass  through  a  soft,  pasty  stage  as  the  melting  point  is  ap- 
proached. In  the  case  of  some  substances,  such  as  the  fats, 
the  melting  point  is  not  the  same  as  the  freezing  point. 
Thus  butter  will  melt  between  28°  and  33°  C  and  yet  solidi- 
fies between  20°  and  23°  C. 

There  are  several  alloys  of  metals  which  melt  at  a  much  lower 
temperature  than  any  of  the  metals  of  which  they  are  made. 
"  Wood's  metal "  (2  tin  +  4  lead  +  7  bismuth  +  1  cadmium 
by  weight)  melts  at  70°  C,  although  the  lowest  melting  point 
of  any  of  its  constituents  is  that  of  tin  (232°  C).  Wood's 
metal  will  melt  even  in  hot  water.  Such  alloys  are  used  to 
seal  tin  cans  and  automatic  fire  sprinklers.  Other  similar 
alloys  are  used  for  fusible  plugs  for  boilers. 

193.  Expansion  in  freezing.  When  a  liquid  freezes,  we 
would  naturally  expect  it  to  contract,  because  it  would  seem 
that  the  molecules  would  be  more  closely  knit  together  in  the 
solid  than  in  the  liquid  state.  This  is  generally  true.  But 
when  we  recall  that  ice  floats  and  pitchers  of  water  are  often 
cracked  by  freezing,  we  see  that  water  expands  on  freezing. 


WATER,   ICE,  AND  STEAM 


201 


In  fact  a  cubic  foot  of  water  becomes  1.09  cubic  feet  of  ice. 
Cast  iron  is  another  substance  that  expands  a  little  in 
solidifying,  and  it  is  therefore  adapted  to  making  castings, 
for  in  this  way  every  detail  of  the  mold  is  sharply  re- 
produced. In  making  good  type  we  must  have  a  metal 
which  expands  a  little  on  solidifying,  and  so  an  alloy  of  lead, 
antimony,  and  copper,  which  has  this  property,  is  used. 

That  the  expansive  force  of  water  in  freezing  is  enormous 
can  be  seen  from  the  following  experiment. 

Let  us  fill  a  cast-iron  bomb  with  water,  close  the  hole  with  a  screw 
plug  (Fig.  168),  and  put  the  bomb  in  a  pail  of  ice 
and  salt.     When  the  water  in  the  bomb  freezes,  the 
pressure  inside  increases  more  and  more,  and  the 
bomb  eventually  explodes. 


This  shows  why  water  pipes  burst  on 
nights  cold  enough  to  freeze  the  water  in 
them.  A  similar  process  is  active  every 
winter  in  breaking  the  rocks  of  mountains 
to  pieces.  Water  percolates  into  the  crev-  FlG-  168-~  ExPan- 

„  ,  sive  force  exerted 

ices,  freezes,  and  expands.  by  freezing  water. 

194.  Effect  of  pressure  on  melting  ice.  If  we  suspend  a  weight 
of  40  or  50  pounds  by  a  wire  loop  over  a  block  of  ice  (Fig.  169),  the  wire 
will  cut  slowly  through  the  ice.  The  pressure  causes  the  ice  to  inelt 
under  the  wire  ;  but  the  water  flowing  around  the  wire  freezes  again 

above  it,  and   leaves  the  block  as  solid   as    be- 

fore. 

This  experiment  shows  that  pressure 
causes  ice  to  melt  by  lowering  the  freez- 
ing point.  This  might  be  expected,  for 
pressure  on  any  body  tends  to  prevent 
its  expansion,  and  since  water  does  ex- 
pand on  freezing,  pressure  will  tend  to 
prevent  freezing  ;  that  is,  it  lowers  the 
It  requires,  however  a 


.  169.  -Wire  cutting 
through  a  block  of  ice.    pressure  of  almost  a  ton  (1850  pounds) 


202  PRACTICAL  PHYSICS 

per  square  inch  to  lower  the  freezing  point  one  degree  Cen- 
tigrade. 

In  skating,  the  pressure  of  the  edge  of  the  skate  blade 
melts  the  ice  and  so  forms  a  film  of  water  which  is  very  slip- 
pery. This  also  explains  how  snowballs  can  be  made  by 
pressing  the  snow  between  the  hands.  The  pressure  at  the 
points  of  contact  between  the  flakes  of  snow  melts  them  and 
then  the  film  of  water  that  is  formed  freezes  again  when  the 
pressure  is  released.  The  flow  of  glaciers  of  solid  ice  around 
corners  is  explained  in  the  same  way. 

195.  Latent  heat :  ice  to  water.     If  a  dish  of  ice  and  water 
at  0°  C  is  kept  in  a  room  where  everything  else  is  at  0°,  the 
ice  will  not  melt  and  the  water  will  not  freeze.     But  if  the 
dish  is  surrounded  by  a  freezing  mixture,  such  as  salt  and  ice, 
the  water  will  freeze,  or  if  the  dish  is  brought  into  a  warm 
room,  the  ice  will  melt.     In  either  case,  however,  the  temper- 
ature of  the  mixture  will  remain  steady  at  0°  until  either  all 
the  ice  is  melted  or  all  the  water  is  frozen. 

It  seems  evident,  then,  that  when  ice  melts,  heat  energy, 
called  latent  heat,  is  absorbed,  which  does  not  show  itself  in  a 
rise  of  temperature. 

196.  How  much  heat  to  melt  1  gram  of  ice  ?     In  solving 
this  problem  we  may  apply  the  method  of  mixtures  which 
was  used  in  determining  the  specific  heat  of  a  metal. 

If  we  put  200  grains  of  ice  at  0°C  into  300  grams  of  water  at  70°  C 
and  stir  them  thoroughly,  the  temperature  of  the  water,  after  the  ice  is 
all  melted,  will  be  10°  C. 

Let  x  —  no.  of  calories  required  to  melt  1  g.  of  ice. 

Then  200  x  =  no.  of  calories  required  to  melt  200  g.  of  ice. 

Also  200  x  10  =  no.  of  calories  required  to  raise  melted  ice  from  0° 

to  10°, 

and     300  (70  -  10)  =  no.  of  calories  given  out  by  the  water  in  cooling. 
Then  200  x  +  200  x  10  =  300  (70  -  10), 

whence  x  =  80  calories. 


WATER,   ICE,   AND   STEAM 


203 


The  best  experiments  that  have  been  made  show  that  the 
latent  heat  of  melting  ice  is  just  about  80  calories,  which 
means  that  80  calories  are  absorbed  in  changing  1  gram  of 
ice  at  0°  C  into  water  at  0°  C. 

197.  Heat  given  out  when  water  freezes.  We  have  just 
seen  that  heat  energy  is  required  to  pull  apart  the  molecules 
of  the  solid  ice  and  change  it  into  the  liquid  state,  where  we 
believe  the  molecules  are  held  together  less  intimately. 
Now  we  want  to  show  that  in  the  reverse 
process,  that  is,  in  freezing,  this  energy  ap- 
pears again  as  heat.  We  may  show  that 
freezing  is  a  heat-evolving  process  in  the 
following  experiment. 

If  we  repeat  the  experiment  described  in  section 
192,  except  that  we  keep  the  water,  thermometer,  and 
test  tube  (Fig.  170)  very  quiet,  we  shall  be  surprised 
to  find  that  the  water  will  cool  several  degrees  below  0° 
C  before  the  freezing  begins.  When  once  started  by 
stirring  or  dropping  in  a  crystal  of  ice,  the  crystals  of 
ice  form  rapidly,  but  the  temperature  jumps  to  0°  C 
and  remains  stationary  until  all  the  water  is  frozen, 
even  though  the  freezing  mixture  in  the  jar  outside 
the  test  tube  is  as  cool  as  —  10°  C. 

People  sometimes  make  use  of  the  heat  given  out  by  water 
when  it  freezes,  by  putting  pails  or  tubs  of  water  in  a  green- 
house or  a  cellar  to  prevent  the  freezing  of  the  plants  or 
vegetables.  As  the  water  begins  to  freeze  first,  the  heat 
evolved  in  the  process  prevents  the  temperature  from  falling 
much  below  0°  C.  When  a  large  lake  freezes,  the  heat 
evolved  helps  to  keep  the  temperature  in  its  vicinity  from 
falling  as  low  as  it  does  farther  away. 

PROBLEMS 

1.  How  many  calories  of  heat  are  required  to  melt  20  grams  of  ice  at 
0°C? 

2.  How  much  heat  is  evolved  in  cooling  and  freezing  12  grams  of 
water  originally  at  10°  C  ? 


17Q  _  Freezjng 
water  evolves  heat. 


204 


PRACTICAL  PHYSICS 


3.  How  many  B.  t.  u.  are  required  to  melt  one  pound  of  ice  at  0°  C  ? 

4.  How  much  water  at  100°  C  will  be  needed  to  melt  300  grams  of 
snow  at  0°  C,  and  raise  its  temperature  to  20°  C  ? 

5.  If  a  500-gram  iron  weight  is  heated  to  250°  C  and  placed  on  a 
block  of  ice,  how  many  grams  of  the  ice  will  be  melted  ? 

198.  Process  of  boiling  water.  Let  us  fill  a  round-bottomed  flask 
(Fig.  171)  half  full  of  water  and  put  through  the  stopper  a  thermometer, 
an  open  manometer,  and  an  outlet  tube  for 
the  steam.  At  first,  as  the  water  is  heated, 
the  air,  which  is  dissolved  in  the  water,  rises 
to  the  surface  in  little  bubbles.  Then  bubbles 
of  steam  form  at  the  bottom,  but  these  col- 
lapse when  they  strike  the  upper,  cooler  layers 
of  water,  and  disappear,  causing  the  rattling 
noise  known  as  "singing"  or  "simmering." 
When  the  bubbles  of  steam  begin  to  reach 
the  surface,  the  water  is  said  to  "boil."  It 
will  be  noticed  that  the  steam  in  the  flask  is  as 
clear  as  air,  but  as  it  leaves  the  outlet  tube  it 
condenses  and  forms  a  white  cloud  or  mist. 

As  soon  as  boiling  begins,  the  thermometer, 
which  has  been  rising  rapidly,  reaches  100°  C 
and  remains  stationary. 
~/~~^   4^1_^S^'^^fl         If    we   partly  close   the  outlet  valve,  the 
»         manometer  will  show  an  increase  of  pressure, 
while  the  thermometer  will  show  a  rise  in  the 
temperature  of  the  boiling  water. 


FIG.  171.  —  Boiling  water. 


Finally  if  we  remove  the  burner,  and  let  the  water  cool  a  bit,  we  may 
connect  the  outlet  tube  with  an  aspirator,  which  will  reduce  the  pressure 
and  make  the  water  boil  again. 

The  process  of  boiling  consists  in  the  formation  in  a 
liquid  of  bubbles  of  vapor,  which  rise  to  the  surface  and  es- 
cape. The  temperature  at  which  this  takes  place  is  the 
boiling  point  of  the  liquid. 

There  is  a  second  and  more  exact  definition  of  the  boiling 
point.  It  is  evident  that  a  bubble  of  water  vapor  can  exist 
within  the  liquid  only  when  the  pressure  exerted  outward 
by  the  vapor  within  the  bubble  is  at  least  equal  to  the  atmos- 
pheric pressure  pushing  down  on  the  surface  of  the  liqui.d. 


WATER,   ICE,  AND   STEAM  205 

For  if  the  pressure  within  the  bubble  were  less  than  the  outside 
pressure,  the  bubble  would  immediately  collapse.  Now  the 
pressure  that  would  exist  inside  a  bubble,  if  it  could  form  at 
all,  would  be  different  at  different  temperatures.  It  is  called 
the  vapor  pressure,  or  vapor  tension,  of  the  liquid,  and  we  shall 
soon  see  how  to  determine  its  values  at  different  temperatures. 
The  boiling  point  of  a  liquid  may  therefore  be  defined  as  the 
temperature  at  which  its  vapor  pressure  is  one  atmosphere. 

199.  Effect  of  changing  pressure.  We  have  just  seen  in 
the  experiment  about  boiling  that  if  the  pressure  on  the 
surface  of  the  liquid  is  increased,  the  temperature  has  to  be 
raised  before  the  liquid  will  boil.  If  the  pressure  is  de- 
creased, the  liquid  will  boil  at  a  lower  temperature.  We 
can  understand  this  if  we  recall  that  ordinarily  the  atmos- 
phere is  exerting  a  pressure  of  about  15  pounds  per  square  inch 
on  the  surface  of  the  liquid.  If  we  reduce  this  pressure,  it 
is  easier  for  the  bubbles  of  vapor  to  form ;  if  the  pressure  is 
increased,  it  is  more  difficult  for  the  bubbles  to  form.  In 
any  case,  they  will  form  only  when  the  temperature  is  high 
enough  so  that,  when  they  have  formed,  the  pressure  in 
them  is  equal  to  the  pressure  on  the  surface  of  the  liquid. 
So  by  observing  the  temperatures  at  which  a  liquid  boils 
under  different  pressures,  we  can  determine  how  the  vapor 
pressure  of  the  liquid  changes  with  temperature.  Experi- 
ments have  shown  that,  near  100°  C,  the  vapor  pressure  of 
water  increases  by  about  27  millimeters  of  mercury  for  each 
Centigrade  degree  rise  of  temperature. 

Benjamin  Franklin  devised  the  following  interesting  ex- 
periment to  show  water  boiling  under  reduced  pressure. 

Let  a  flask  half  full  of  water,  which  is  boiling  vigorously,  be  removed 
from  the  flame  and  instantly  corked  air-tight  with  a  rubber  stopper.  We 
may  then  invert  the  flask,  as  shown  in  figure  172,  and  cool  the  top  by 
pouring  on  cold  water.  The  water  in  the  flask  immediately  begins  to 
boil  again.  This  is  because  the  steam  in  the  top  of  the  flask  is 
condensed  and  so  the  pressure  on  the  surface  of  the  liquid  is  much 
reduced. 


206 


PRACTICAL  PHYSICS 


Sometimes  it  is  very  desirable  to  boil  liquids  at  as  low 
a  temperature  as  possible.  For  example,  the  water  is 
boiled  away  from  sirup  and  from  milk  in 
what  are  called  vacuum  pans,  which  are  merely 
closed  kettles  with  part  of  the  air  pumped 
out.  The  water  boils  away  at  about  70°  C 
and  leaves  the  granulated  sugar  or  milk 
condensed,  but  not  cooked. 

On  the  tops  of  high  mountains  the  temper- 
ature of  boiling  water  is  so  low  that  eggs 
cannot  be  cooked.     In  Cripple  Creek,  Col., 
about  10,000  feet  above  sea  level,  it  takes 
about  twice  as  long  to  cook  potatoes  as  in 
Boston.     In  some  high  altitudes  closed  ves- 
FIG.  172.  —  Boiling    sels    provided    with     safety    valves,    called 
water  under  re-    "digesters"  or  "pressure  cookers"  (Fiff.  173), 

duced  pressure.      ,  , 

nave  to  be  used  in  cooking.  Digesters 
are  also  used  for  extracting  gelatine  from  bones.  The 
effect  of  the  increased  pressure  in  a  digester  or  pressure 
cooker  is  the  same  as  in  a  boiler.  The  water  in  a  boiler 
whose  gauge  reads  100  pounds  is  boil- 
ing, not  at  100°  C,  but  at  170°  C  or 
338°  F. 

Since  we  have  denned  the  100°  point 
on  the  Centigrade  scale  as  the  tempera- 
ture of  boiling  water,  and  since  the  tem- 
perature at  which  water  boils  is  so  much 
affected  by  changes  in  pressure,  it  is 
necessary  to  fix  on  some  standard  pressure 
at  which  thermometers  are  to  be  "  cali-  FlG-  173-  —  Pressure 
brated"  or  marked.  By  common  agree- 
ment, this  standard  pressure  is  the  pressure  exerted  by  a 
column  of  mercury  760  millimeters  high,  the  temperature  of 
the  mercury  being  0°  C.  The  temperature  at  which  water 
boils  under  this  pressure  is,  by  definition,  100°  C. 


WATER,   ICE,   AND   STEAM 


207 


200.    Summary.     What  has  been  said  about  the  process  of 
boiling  can  be  summarized  as  follows  :  — 

(1)  A  liquid  will  boil  only  when  its  temperature  is  such  that 
its  vapor  pressure  is  equal  to  the  pressure  on  its  surface. 

(2)  What  is  called  "  the  boiling  point "  of  a  liquid  is  the 
temperature  at  which  it  will  boil  under  atmospheric  pressure  ; 
that  is,  the    temperature    at   which   its  vapor  pressure  is  one 
atmosphere,  or  760  millimeters  of  mercury. 

(3)  Every  liquid  has  its  own  boiling  point.      The  boiling 
point  of  water  is  by  definition  100°  O. 

(4)  The  rule  about  boiling  under  other  pressures  than  one 
atmosphere  is,  the  higher  the  pressure,  the  higher  the  tempera- 
ture required  to  make  the  liquid  boil. 


TABLE  OF  BOILING  POINTS 

(At  a  pressure  of  760  millimeters  ) 


Zinc  918°  C 

Sulphur  445°  C 

Mercury  357°  C 

Saturated  salt  solution  108°  C 

Water  100°  C 


Alcohol 

Ether 

Ammonia 

Oxygen 

Hydrogen 


78°  C 
35°  C 

-  34°  C 
- 183°  C 

-  253°  C 


201.    Distillation.     In  many  localities  the  only  way  to  be 
sure  of  getting  pure  water  is  by  what  is  called  distillation. 

Let  us  set  up  a  boiler  B  and 
a  condenser  C  as  shown  in 
figure  174,  and  color  the  water 
in  the  boiler  with  blue  vitriol 
(copper  sulphate).  When  the 
solution  is  boiled,  the  vapor 
or  steam  given  off  is  con- 
densed, by  the  continual  cir- 
culation of  cold  water  through 
the  jacket,  as  a  colorless,  taste-  Fm  174._Purification  of  water  by  distillation, 
less  liquid,  pure  or  distilled 

water.     The  non-volatile  impurities,  including  the  vitriol,  are  left  behind 
in  the  boiler. 


208 


PRACTICAL  PHYSICS 


The  process  of  distillation  consists 
of  boiling  a  liquid  and  condensing 
its  vapor.  In  commercial  work  this 
is  usually  done  in  a  "worm  con- 
denser." This  consists  of  a  pipe 
coiled  into  a  spiral  and  surrounded 
by  circulating  cold  water  (Fig 
175).  In  this  way  a  large  condens- 
ing surface  is  obtained  in  a  small 
space. 

When  a  mixture  of  two  liquids  is 
distilled,  the  liquid  with  the  lower 
boiling  point  vaporizes  and  is  con- 
densed first.     It  can  thus  be  sepa- 
rated from  the  one  with  the  higher 
boiling    point.       Thus     alcohol     is 
Fia.  175.— Worm  condenser,     distilled    from     fermented    liquors 
by  this   process  of   fractional  distillation.     It   is    in   this   way 
that  gasolene  and  kerosene  are  got  from  crude  petroleum. 


PROBLEMS  AND  QUESTIONS 

1.  How  is  the  temperature  of  boiling  water  affected  by  taking  the 
water  to  the  bottom  of  a  deep  mine  ? 

2.  If  water  boils  at  99°  C,  what  is  the  atmospheric  pressure  ? 

3.  If  water  boils  at  208°  F,  what  does  the  barometer  read  ? 

4.  An  elevation  of  900  feet  makes  a  difference  of  about  1  inch  in  the 
barometer.     At  what  temperature  would  water  boil  1500  feet  above  the 
sea? 

5.  What  effect  does  salt  or  sugar  have  oh  the  boiling  point  of  water  ? 
Try  it. 

6.  In  distilling  a  mixture  of  alcohol  and  water,  which  liquid  begins 
to  distill  over  first  ? 

7.  How  could  you  obtain  fresh  water  from  sea  water? 

8.  Mark  Twain  in  his  "  Tramp  Abroad  "  tells  of  stopping  on  his  way 
up  a   mountain   to   "  boil  his  thermometer."     What   did   he   do,   and 
why? 


WATER,   ICE,   AND   STEAM  209 

202.  Latent   heat :    water   to   steam.     When   a   kettle  of 
water  is  put  on  a  stove,  it  gets  hotter  and  hotter  until  it 
boils.     Then  no  matter   how  much   heat  we   apply  to   the 
kettle,  if  there  is  a  free    outlet   for   the    steam    to  escape, 
the    temperature    remains   constant  at    100°    C  or  212°    F. 
The  heat  energy  which  seems  to   disappear  in  boiling  the 
water  is  called  the  latent  heat  of  steam  or  the  latent  heat  of 
vaporization.     When  steam  flows  from  a  steam  pipe  into  a 
radiator  in  a  room,  some  of  it  condenses  and  gives  back  the 
heat  which  apparently  disappeared  when  the  water  changed 
into  steam.     This  latent  (or  hidden)  heat  is  now  understood 
to   represent   the   energy  needed   to   pull  the  molecules  of 
water  away  from  each  other  and  set  them  free  as  steam. 

203.  How  much  heat  is  needed  to  make  a  gram  of  steam? 
When  we  want    to   determine  the  amount  of    heat  needed 
to  change  a  gram  of  water  at  100°  C  into  steam  at  100°  C, 
we  usually  apply  the  method  of  mixtures.     In  practice  we 
generally  try  to  determine  the  heat  evolved  in  condensing  a 
gram  of  steam  by  running  dry  steam  into  a  given  quantity 
of  water  at  a  known  temperature  for  some  time.     We  meas- 
ure the  rise  in  temperature  and  the  increase  in  weight,  which 
is  the  weight  of  the  condensed  steam.     Then  we  make  an 
equation  in  which  the  number  of  calories  received  by  the 
water  in  being  warmed  is  put  equal  to  the  calories  given  out 
by  the  steam  in  condensing  to  water  at  100°  C  and  by  this  hot 
water  in  cooling  from  100°  C  to  the  temperature  of  the  mixture. 

Suppose  we  take  400  grams  of  water  at  5°  C  and  run  in  20  grams  of 
steam  at  100°  C,  which  raises  the  temperature  of  the  water  to  35°  C. 
What  is  the  number  of  calories  of  heat  given  out  by  1  gram  of  steam  in 
condensing  to  water  at  100°  C  ? 

Let  x  =  latent  heat  of  steam. 

Since    400  (35  —  5)  =  heat  absorbed  by  cold  water, 
and  20  x  —  heat  given  out  by  condensing  of  steam, 

and      20(100-35)  =  heat  given  out  by  water  in  cooling  from  100°  to  35°  C, 
then     400(35  -  5)  =  20  x  +  20(100-35), 
and  x  =  535  calories. 


210  PRACTICAL  PHYSICS 

Recent  experiments  have  shown  that  the  latent  heat  oi 
steam  is  about  540  calories.  In  other  words,  it  takes  more 
than  five  times  as  much  heat  to  change  any  quantity  of  water 
into  steam  as  to  raise  the  same  quantity  of  water  from  the  freez- 
ing to  the  boiling  point.  In  English  units  it  requires  540  x  1. 8 
or  972  B.  t.  u.  to  change  a  pound  of  water  at  212°  F  into 
steam  at  212°  F. 

PROBLEMS 

1.  Find  the  number  of  calories  required  to  change  15  grams  of  water 
at  100°  C  into  steam. 

2.  Compute  the  heat  evolved  by  condensing  10  grams  of  steam  at 
100°  C  and  cooling  it  down  to  50°  C. 

3.  How  much  heat  will  be  required  to  convert  1  kilogram  of  ice  at 
0°  C  into  steam  at  100°  C? 

4.  How  much  steam  at  100°  C  must  be  run  into  500  grams  of  water  at 
10°  to  raise  it  to  40°  V 

5.  In  the  illustrative  example  in  section  203,  the  latent  heat  came  out 
535,  which  is  a  little  too  low.     This  shows  that  the  temperature  of  the 
mixture  (35°  C)  was  not  acccurately  observed.     What  should  it  have 
been  ? 

6.  How  many  pounds  of  coal  will  be  needed  in  a  boiler  whose  efficiency 
is  65%,  to  convert  100  pounds  of  water  at  50°  F  into  steam  at  212°  F? 
Assume  that  the  heat  value  of  the  coal  is  14,500  B.  t.  u.  per  pound. 

204.  Evaporation.     Everybody  is  familiar  with  the  fact 
that   water  left  in  an  open  dish   gradually   disappears   or 
evaporates.     Evaporation  is  different  from  boiling,  in  that  evap- 
oration takes  place  at  any  temperature  but  only  at  the  surface 
of  a  liquid,  while  boiling  goes  on  inside  the  liquid  but  only 
at  a  fixed  or  definite   temperature.     Evaporation  goes  on 
more  rapidly  the  warmer  and  drier  the  surrounding  air  is. 
For  example,  wet  clothes  dry  more  quickly  on  a  hot  day  than 
on  a  cold,  foggy  day. 

205.  Cooling  by  evaporation.     If  one  pours  a  few  drops  of 
alcohol  or  ether  on  his  hand,  the  liquid  quickly  evaporates, 
causing  a  markecj.  sensation  of  cold.     Whenever   a   liquid 
evaporates,  it  must  get  heat  from  somewhere,  and  so  the 


WATER,  ICE,  AND   STEAM  211 

temperature  of  the  liquid  itself  and  of  anything  near  it  drops. 
That  is  to  say,  heat  is  absorbed  in  the  process  of  evaporation. 
It  is  always  more  comfortable  on  a  hot  day  to  ride  in  a  car 
than  to  sit  still,  because  the  rapid  circulation  of  the  air  makes 
the  moisture  of  the  skin  evaporate  more  rapidly.  This  is 
why  one  can  tell  the  direction  of  the  wind  by  lifting  a 
moistened  finger;  the  wind  blows  from  the  side  which  feels 
cool. 

206.  Moisture  in  the  air.  In  the  summer  time  a  pitcher  of 
ice  water  is  usually  covered  with  little  drops  of  water  or 
"sweat."  It  might  at  first  be  thought  that  these  were  due 
to  the  water  oozing  through  the  pores  in  the  side  of  the 
pitcher ;  but  the  microscope  does  not  show  any  pores  in  glazed 
porcelain  or  glass,  so  we  must  conclude  that  the  drops  come 
from  the  surrounding  air.  The  air  is  cooled  by  coming  in 
contact  with  the  cold  pitcher  and  deposits  some  of  its  mois- 
ture. If  we  put  a  little  water  in  a  bottle  and  cork  it  tightly, 
the  water  does  not  evaporate  because  the  air  above  the  water 
quickly  becomes  "saturated"  with  moisture.  Thus  we  see 
that  air  can  take  up  only  a  definite  quantity  of  moisture, 
depending  on  the  temperature.  This  can  be  better  under- 
stood from  the  following  experiment. 

Let  us  place  a  little  water  in  a  thin -walled  flask  and  cork  it.  If  we 
place  tne  cask  in  a  warm  place  until  it  becomes  warm,  and  then  cool  it, 
its  walls  become  dim,  due  to  the  drops  of  water.  The  warm  saturated 
air  becomes  "  supersaturated  "  on  cooling. 

Careful  experiments  show  that  a  cubic  meter  of  saturated 
air  contains  at  different  temperatures  the  following  amounts 
of  water  vapor:  — 

2  grams  at  -  10°  C. 

5  grams  at         0°  C. 

9  grams  at       10°  C. 

17  grams  at      20°  C. 

30  grams  at       30°  C. 

597  grams  at     100°  C. 


212 


PRACTICAL   PHYSICS 


From  this  table  it  will  be  seen  that  air,  which  is  saturated 
at  one  temperature,  can,  at  a  higher  temperature,  take  up  still 
more  water  vapor  before  becoming  saturated  ,•  but  if  cooled,  it 
must  deposit  some  of  the  water  vapor  which  it  already  has. 

207.  Relative  humidity.  Usually  the  air  does  not  contain 
all  the  moisture  which  it  can  hold  ;  that  is,  it  is  not  saturated. 
If,  however,  the  temperature  suddenly  drops,  the  same  ac- 
tual amount  of  moisture  will  saturate  the  air. 

For  example,  if  the  water  in  a  polished  nickel-plated  cup  is  cooled 
with  ice  below  the  temperature  of  the  room,  a  mist  will  appear  on  the 
outside  of  the  beaker.  The  temperature  of  the  water  when  this  occurs  is 
the  "  dew  point." 

The  dew  point  is  the  temperature  at  which  the 
water  vapor  in  the  air  begins  to  condense.  If 
the  air  is  cooled  below  the  dew  point,  some  of 
its  vapor  condenses,  and  dew  collects  on  objects. 
Thus  we  see  that  the  words  "  dry  "  or  "moist," 
as  applied  to  the  atmosphere,  have  a  purely  rel- 
ative significance.  They  involve  a  comparison 
between  the  amount  of  water  vapor  actually 
present,  and  that  which  the  air  could  hold  if 
saturated  at  the  same  temperature.  The  ratio 
of  these  two  quantities  is  called  the  relative 
humidity.  For  example,  we  may  read  in  the 
newspaper  that  the  relative  humidity  is  75%. 
This  means  that  the  amount  of  water  vapor 
actually  present  in  the  air  is  75  %  of  what  the 
air  might  have  contained  at  the  given  tempera- 
ture if  it  had  been  saturated. 

208.   Wet  and  dry  bulb  thermometers.    Let  two 

thermometers  be  arranged  as  shown  in  figure  176.  The  bulb 
of  the  thermometer  at  the  left  is  dry,  while  the  other  ther- 
mometer has  its  bulb  wrapped  with  cotton  cloth  which  is 
kept  moist  by  a  cup  of  water.  If  we  keep  the  air  around 
the  thermometers  circulating  by  an  electric  fan,  after  a 


ra 

1 

g 

s 

0 

i 

s 

I. 

I 

a 
s 

j£ 

-^ 

jj 

1 

nr 

7>r2/         JFe< 

FIG.  176;  —  Wet 
and  dry  bulb 
thermometers. 

WATER,   ICE,  AND  STEAM  213 

little  while  the  wet-bulb  thermometer  will  indicate  a  lower  temperature 
than  the  dry-bulb  thermometer.  This  is  because  of  the  cooling  caused 
by  the  evaporation  from  the  cotton  cloth.  The  drier  the  surrounding  air, 
the  more  rapid  will  be  the  evaporation,  and  so  the  greater  will  be  the 
difference  between  the  wet  and  dry  bulb  thermometers.  With  the  aid 
of  tables  furnished  by  the  Weather  Bureau,  we  may  determine  from 
these  thermometer  readings  the  so-called  "  relative  humidity  "  of  the  air. 

209.  Practical  importance  of  determining  humidity.   It  is  well 
known  that  a  hot  day  in  Boston  is  much  more  uncomfortable 
than  an  equally  hot  day  in  Denver.     This  is  because  a  city 
near  the  ocean,  like  Boston,  has  a  higher  relative  humidity 
than  a  city  which  is  inland  and  a  mile  above  sea  level,  like 
Denver.     When    the    relative    humidity    is   high,    we    feel 
"  sticky  "  because  the  perspiration  of  the  skin  does  not  evap- 
orate readily.     On  the  other  hand,  too  little  humidity  is  in- 
jurious.    Special  precautions  are  taken  to  keep  the  air  in 
schools,  hospitals,  and  private  houses  from  getting  too  dry  in 
winter,  and  the  air  in  greenhouses  must  be  kept  quite  damp  for 
the  growth  of  plants.     In  cotton  mills  it  has  been  found  that 
the  air  must  be  rather  moist  to  make  the  spinning  of  yarn  suc- 
cessful. 

Since  the  occurrence  of  frost  in  the  late  spring  or  early 
fall  is  injurious  to  many  crops,  it  is  often  highly  important 
that  farmers  should  know  in  the  afternoon  whether  freezing 
weather  during  the  night  is  to  be  expected.  The  tempera- 
ture of  the  dew  point  gives  a  ready  means  of  predicting  how 
low  the  temperature  at  night  will  drop ;  for  when  the  dew 
point  is  reached,  further  cooling  is  retarded.  So  if  the  dew 
point  is  above  40°  F,  it  is  seldom  that  the  temperature  will 
fall  to  freezing  in  the  night. 

210.  Dew,  fog,  rain,  and  snow.     On  clear,  still  nights  the 
ground  radiates  the  heat    that  it  has  received   during  the 
daytime.    The  grass  and  leaves,  which  can  radiate  heat  freely, 
cool  rapidly  and  soon  bring  the  air  near  them  below  its  dew 
point.     Then   moisture  condenses,  as  dew  or  at  lower   tern- 


214  PRACTICAL   PHYSICS 

peratures  as  frozen  dew  or  frost.  This  phenomenon  is  exactly 
like  the  formation  of  drops  of  water  on  a  pitcher  of  ice 
water,  or  on  one's  spectacles  when  he  conies  from  the  cold  out- 
doors into  a  warm  room.  Clouds  covering  the  sky  hinder 
the  formation  of  dew  because  they  restrict  radiation.  If  the 
condensation  of  the  moisture  of  the  air  is  not  brought  about 
by  contact  with  cold  solid  objects  at  the  surface  of  the  earth, 
but  by  great  masses  of  cold  air  high  above  the  earth,  clouds 
are  formed  and  rain  may  result.  Fog  is  merely  clouds  very 
near  the  earth. 

Clouds  at  very  high  altitudes  may  be  composed  of  bits  of 
ice,  but,  in  general,  clouds  are  made  up  of  minute  drops  of 
water.  Like  particles  of  fine  dust,  very  small  drops  of  water 
tend  to  fall,  but  can  do  so  only  very  slowly.  Sometimes  they 
fall  into  warm  and  not  yet  saturated  layers  of  air,  and  then 
they  change  back  again  into  vapor.  Sometimes  they  are 

carried  up  by  ascending 
currents  of  air  faster  than 
they  can  fall  through 
them,  and  so  seem  to 
float.  For  example,  the 
cloud  of  steam  above  a 
locomotive  stack  is  com- 
posed of  minute  drops  of 
water  and  yet  rises  with 
the  warm  air.  Clouds 
are  not  durable.  They 
simply  mark  the  place  in 
the  atmosphere  where  the 
process  of  condensation 
of  water  vapor  is  going 
on.  In  rain  clouds  the 
little  particles  of  water 
come  together  and  form 
FIG.  177.— Snow  crystals.  drops  which  easily  over- 


WATER,  ICE,   AND   STEAM  215 

come  the  resistance  of  the  air  and  fall  to  the  ground.  If  the 
temperature  of  the  cloud  is  below  32°  F,  the  particles  of 
water  unite  to  form  little  delicately  fashioned  hexagonal 
snow  crystals  (Fig.  177). 

Snow  and  rain  together  make  what  the  "  weather  man " 
calls  "precipitation."  Thus  in  New  York  there  are  about 
150  days  of  rain  or  snow  each  year,  and  the  total  precipitation 
in  a  year,  if  it  did  not  dry  up,  would  cover  the  earth  to  a 
depth  of  about  3  feet. 


QUESTIONS  AND  PROBLEMS 

1.  A  room  is  3  meters  high,  10  meters  long,  and  6  meters  wide.    How 
many  grams  of  water  will  be  required  to  saturate  the  air  at  20°  C  ? 

2.  An  experiment  showed  that  on  a  certain  day,  when  the  tempera- 
ture was  30°  C,  the  air  contained  12  grams  of  water  per  cubic  meter. 
What  was  the  relative  humidity? 

3.  How  do  undue  dryness  and  undue  dampness  affect  wooden  furni- 
ture? 

4.  What   change  in  the  thermometer  usually  goes  with  a  rising  ba- 
rometer ? 

5.  What    happens  when    a   moist  wind  from   the   ocean   strikes    a 
mountain  range  ? 

6.  In  some  hot  countries   the   people   cool  their  drinking  water  by 
setting  it  in  jars  of  porous  earthenware,  in  a  shady  place,  where  there  is 
a  current  of  air.     Explain. 

7.  Milk  used  to  be  set  away  in   shallow  pans  for  the  cream  to  rise. 
Now  they  use  cylindrical  tanks  of  small  area  and  quite  deep.     Which  is 
the  better,  and  why? 

8.  Why  do  clothes  dry  best  on  a  windy  day  ? 

9.  Why  does  sprinkling  the  street  on  a  hot  day  cool  the  air? 

211.  Freezing  by  boiling.  The  fact  that  a  large  quantity 
of  heat  is  needed  to  vaporize  a  substance  is  often  made  use 
of  in  getting  low  temperatures. 

If  a  cylinder  of  liquefied  carbon  dioxide  is  tilted,  as  shown  in  figure 
178,  and  the  valve  is  opened,  the  liquid  released  from  pressure  vaporizes 
so  rapidly  as  to  cool  everything,  including  the  rest  of  the  liquid,  and  so 


216 


PRACTICAL   PHYSICS 


some  of  it  is  frozen.  After  the  valve  has  been  open  a  short  time,  the 
bag  is  tilled  with  a  white  solid,  frozen  carbon  dioxide.  This  solid  evap- 
orates very  readily,  and  gives  a  temperature  as  low  as  —  80°  C.  If  the 
solid  is  put  in  a  beaker  and  mixed  with  ether, 
the  mixture  will  freeze  a  test  tube  of  mercury.  The 
ether  serves  to  carry  the  heat  quickly  from  the  test 
tube  to  the  solid. 


FIG.  178.  —  Liquid 
carbon  dioxide  be- 
ing frozen. 


212.  Artificial  ice.  In  the  manufacture 
of  artificial  ice  and  in  refrigerating  plants 
(Fig.  179),  gaseous  ammonia  is  compressed 
by  a  pump  and  then  cooled  until  it 
liquefies.  During  this  process  of  com- 
pression and  of  condensation,  heat  is 
evolved,  which  is  removed  by  passing 
the  ammonia  through  a  pipe  covered  with  running  water. 
The  liquefied  ammonia  is  then  piped  to  the  ice  tank  or  cold- 
storage  room,  and  allowed  to  expand  through  a  valve  with  a 
small  opening.  This 
checks  the  flow,  and 
so  enables  the  pump  to 
maintain  enough  pres- 
sure to  keep  the  am- 
monia in  liquid  form 
on  its  way  to  the  valve  ; 
while  beyond  the  valve 
the  pressure  is  very 
small,  so  that  the  am- 
monia expands  and 
evaporates  rapidly. 
While  doing  so,  it 
absorbs  heat  from  the  refrigerating  room.  It  is  then  ready 
to  be  compressed  again. 

In  ths  manufacture  of  ice,  the  expansion  pipes  pass  through 
a  brine  tank  in  which  are  smaller  tanks  of  pure  water. 
When  the  water  in  these  tanks  is  frozen,  the  tanks  are  pulled 
up  and  the  ice  removed  and  stored.  The  ammonia  is  used 


I,  To  sewer 
FIG.  179.  —  Diagram  of  cold-storage  plant. 


WATER,   ICE,  AND  STEAM  217 

over  and  over  again,  but  power  must  be  constantly  supplied 
to  keep  the  compressor  working. 

SUMMARY   OF  PRINCIPLES   IN   CHAPTER  XI 

Heat  units :  — 

1  B.  t.  u.  =  heat  to  raise  1  Ib.  of  water  1°  F. 
1  calorie  =  heat  to  raise  1  gram  of  water  1°  C. 

Specific  heat  =  calories  to  raise  1  gram  of  substance  1°  C. 
Specific  heat  of  water  =  1. 

Method  of  mixtures :  — 

Heat  given  up  by  hot  bodies  =  heat  absorbed  by  cold  bodies. 

Pressure :  — 

Lowers  freezing  point  of  water  0.0072°  C  per  atmosphere. 
Raises  boiling  point  of  water  0.037°  C  per  millimeter  of  mercury. 

Latent  heat  of  melting  =  heat  absorbed  during  melting, 

=  heat  yielded  during  freezing. 
Value  for  water,  80  calories. 

Latent  heat  of  vaporization  =  heat  absorbed  during  evaporation, 

=  heat  yielded  during  condensation. 
Value  for  water,  640  calories. 

Relative  humidity 

actual  moisture  in  air 

moisture  sufficient  to  saturate  air  at  same  temp. 

QUESTIONS 

1.  If  you  know  the  dew  point  to  be  10°  C,  how  could  you  find  the  rel- 
ative humidity  at  20°  C  ? 

2.  Human  hair  when   treated  with  ether  is  very  sensitive  to  mois- 
ture.    When   it  is  moist  it  contracts,  and  when  it  dries  it  elongates. 
Explain  how  a  moisture  gauge  or  "hygrometer"  could  be  made  with  a 
hair. 


218  PEACTICAL  PHYSICS 

3.  Why  do  they  not  cast  gold  money  instead  of  stamping  it  with  a 
die? 

4.  Why  is  a  burn  from  live  steam  so  severe  ? 

5.  Why  does  one  sometimes  "  catch  cold  "  by  sitting  in  a  draft  of 
cool  air  after  taking  violent  exercise  ? 

6.  How  low  may  the  temperature  fall  during  a  rain? 

7.  Why  can  mercury  mixed  with  zinc  and  tin  be  purified  by  distilla 
tion? 

8.  Why  is  it  difficult  to  make  snowballs  out  of  dry  snow? 


CHAPTER   XII 


HEAT  ENGINES 

The  invention  of  the   steam  engine  —  boilers  —  slide-valve 
and  Corliss  engines  —  expansion  —  compounding  —  condensers 

—  efficiency  —  steam  turbines  —  2-cycle  and  4-cycle  gas  engines 

—  balance  sheets  of  engines  —  mechanical  equivalent  of  heat. 

213.  The  invention  of  the  steam  engine.  In  our  age  no 
other  machine  is  of  such  importance  as  the  steam  engine.  It 
furnishes  the  driving  power  for  running  a  countless  number 
of  machines  in  our  shops  and  factories,  as  well  as  for  trans- 
portation on  land  and  sea. 

Up  to  about  two  hundred 
years  ago  steam  had  been  used 
only  in  various  devices,  called 
steam  fountains,  for  raising 
water.  In  1705  the  first  suc- 
cessful attempt  to  combine  the 
ideas  of  these  devices  into  an 
economical  and  convenient  ma- 
chine was  made  by  Thomas  New- 
comen  (1663-1729),  a  blacksmith 
of  Dartmouth,  England.  This 
machine  was  called  an  "  atmos- 
pheric steam  engine"  (Fig.  180). 
It  consisted  of  a  boiler  A,  in 
which  the  steam  was  generated, 
and  a  cylinder  J5,  in  which  a 
piston  moved.  When  the-  valve  V  was  opened,  the  steam 
pushed  up  the  piston  P.  At  the  top  of  the  stroke,  the  valve 

219 


FIG.  180.  —  Newcomen's  steam 
engine. 


220 


PRACTICAL  PHYSICS 


V  was  closed,  the  valve  V  was  opened,  and  a  jet  of  cold 
water  from  the  tank  0  was  injected  into  the  cylinder,  thus 
condensing  the  steam  and  reducing  the  pressure  under  the 
piston.  The  atmospheric  pressure  above  then  pushed  the 
piston  down  again. 

This  machine  was  used  to  pump  water  from  mines.  It 
consumed  a  great  deal  of  fuel,  because  the  cold  water  cooled 

the  cylinder  walls  so  much  that 
when  the  steam  was  turned  in, 
much  steam  condensed  before 
the  piston  was  raised. 

The  next  great  step  in  the 
development  of  the  steam  en- 
gine came  through  a  Scotch  in- 
strument maker,  James  Watt 
(1736-1819).  He  arranged  a 
separate  vessel  for  condensing 
the  steam,  as  shown  in  figure 
181.  This  condenser,  (7,  was 
connected  with  the  cylinder 
through  a  valve  V .  When  the 
piston  had  reached  the  top  of  the 
FIG.  181. -Watt  added  a  separate  cylinder,  the  valve  Fwas  closed 

condenser.  t   -m 

and  V  was  opened.      Then  the 

steam  rushed  from  the  cylinder  into  the  condenser,  which 
was  kept  cold  and  under  less  than  atmospheric  pressure. 
At  first  these  valves  V  and  V  had  to  be  operated  by  hand, 
but  later,  it  is  said,  a  boy  named  Potter,  whose  job  it  was 
to  turn  these  valves,  connected  the  valve  handles  by  cords 
to  the  beam  ED  in  such  a  way  that  the  machine  became 
automatic. 

In  all  these  crude  machines  the  steam  simply  furnished 
the  vacuum,  and  atmospheric  pressure  did  the  work.  Later, 
Watt  made  a  machine  with  a  closed  cylinder  and  a  piston 
that  was  pushed  down  as  well  as  up  by  steam.  By  the  use 


HEAT  ENGINES 


221 


of  a  connecting  rod  and  crank  shaft,  ho  contrived  to  change 
the  back-and-forth  motion  of  the  piston  to  a  rotary  motion, 
and  so  made  the  steam  engine  available  for  many  new  uses. 
Within  a  few  years  the  development  of  the  steam  engine 
revolutionized  most  lines  of  industry. 

214.  A  modern  steam  plant.     In  a  modern  steam  plant  the 
steam  is  made  in  a  boiler,  is  used  in  a  steam  engine,  and  is 
got  rid  of  in  an  exhaust  or  condenser.     We  will  discuss 
these  in  turn. 

215.  Steam  boilers.     A  fire-tube  boiler  consists  of  a  steel  cyl- 
inder which  sometimes  stands  on  end,  as  in  the  small  "  donkey 
engines  "  used  with  derricks,  but  generally  is  set  on  its  side, 


FIG.  182.  —  Section  of  a  locomotive  boiler. 

as  in  locomotives  (Fig.  182).  Running  through  this  cyl- 
inder are  tubes,  three  or  four  inches  in  diameter,  through  which 
the  fire  and  smoke  pass.  The  water  and  steam  fill  the  rest 
of  the  cylinder  outside  the  tubes.  These  tubes  give  the  boiler 
a  much  greater  heating  surface,  so  that  it  makes  more  steam 
per  hour.  Such  boilers  are  called  fire-tube  boilers.  In  an- 
other type,  called  a  water-tube  boiler  (Fig.  183),  the  water  is 
inside  the  tubes  and  the  fire  is  outside.  Such  a  boiler  consists 
of  a  large  number  of  tubes,  inclined  at  an  angle  and  fastened 
at  euch  end  into  vertical  "headers":  these  headers  communi- 


222 


PRACTICAL  PHYSICS 


Steam 


FIG.  183.  —Section  of  water-tube  boiler. 


cate  with  a  drum  above,  which  is  half  full  of  water,  the  re 
mainder  of  the  drum  forming  a  space  for  steam.     The  watei 

descends  by  the 
back  headers, 
rises  through 
the  inclined 
tubes,  and  passes 
up  the  front 
headers,  thus 
maintaining  a 
very  good  circu- 
lation. The  fire 
is  placed  under 
the  front  end  of 
V  the  tubes ;  the 
gases  are  de- 
flected by  brick 
walls,  so  that 
they  pass  completely  over  and  under  the  whole  length  of  the 
tubes.  In  some  water-tube  boilers  the  fire  grate  is  sloping 
and  arranged  like  a  flight  of  steps.  The  coal  is  automati- 
cally fed  through  a  chute  from  the  coal  loft  above  to  the 
grate.  The  principal  advantages  of  this  type  of  boiler  are 
its  great  freedom  from  risk  of  explosion  and  its  ability  to 
make  steam  quickly.  A  modified  form  of  this  boiler  is 
generally  used  in  marine  work. 

Not  only  is  it  desirable  to  get  the  greatest  quantity  of 
steam  with  the  least  expenditure  of  fuel,  but  it  is  also  essen- 
tial to  keep  the  steam  pressure  constant  and  to  prevent  an 
explosion  which  may  have  frightful  consequences.  There- 
fore every  boiler  is  equipped  with  a  steam  gauge,  which  is 
merely  a  Bourdon  pressure  gauge  (section  75),  and  a  water 
gauge  (section  62),  which  enable  the  engineer  in  charge  to 
watch  the  pressure  and  water  level  in  the  boiler.  If  the 
water  level  is  too  low,  there  is  danger  of  burning  the  tubes 


HEAT  ENGINES  223 

and  plates  and  perhaps  of  wrecking  the  boiler ;  if  it  is  too 
high,  water  is  liable  to  be  carried  along  with  the  steam  and 
so  damage  the  engine.  Besides 
these  devices,  every  boiler  must 
have  a  safety  valve,  which  auto- 
matically lets  the  steam  blow 
off  when  the  pressure  exceeds  a 

certain  limit.     A   simple   form 
,       ,,  ,         .       ,  .      £  FIG.  184. -Safety  valve. 

ot  satety  valve  is  shown  m  ng- 

ure  184.     In  some  forms  a  spring  is  set  so  as  to  release  the 

steam  if  the  steam  pressure  becomes  too  great  inside  the 

boiler. 

In  order  to  make  steam  rapidly,  the  fire  must  burn  fiercely, 
which  requires  a  -good  draft.  To  get  this,  tall  chimneys  are 
sometimes  used,  and  at  other  times  a  forced  draft  is  made  by 
a  big  fan.  On  battleships  a  forced  draft  is  often  obtained 
by  making  the  whole  fireroom,  within  which  the  stokers 
work,  air-tight,  and  keeping  it  full  of  air  under  pressure, 
supplied  by  blowers  or  pumps  as  fast  as  it  can  escape  through 
the  fires. 

One  pound  of  coal,  whose  heat  value  is  14,000  B.  t.  u.,  could 
change  14.4  pounds  of  water  at  212°  F  into  steam  at  212°  F 
if  no  heat  were  wasted.  In  actual  practice,  one  pound  of 
coal  evaporates  between  8  and  10  pounds  of  water  "  from  and 
at  212°  F,"  which  means  an  efficiency  of  from  55  to  70%. 
One  great  source  of  loss  of  heat  is  the  flue  gases.  Smoke 
pouring  from  the  chimney  means  that  just  so  much  unconsumed 
fuel  is  going  to  waste,  and,  what  is  worse,  is  adding  to  the 
dirty  atmosphere  of  the  neighborhood.  To-day  steam  engi- 
neers are  able  to  design  boilers  which,  when  properly  stoked, 
produce  no  smoke. 

216.  Steam  engine.  The  type  of  engine  most  commonly 
used  for  small  plants  and  for  locomotives  is  the  slide-valve 
engine  (Fig.  185).  Steam  comes  from  the  boiler  into  a  box 
or  steam  chest,  and  then  into  the  working  end  of  the  cylinder 


224 


PRACTICAL  PHYSICS 


FIG.  185.  —  Slide-valve  steatn  engine. 


through  a  passage  shown  by  the  arrows  at  the  right  of  the 

picture.     At  the  same  time  the  spent  steam  in  the  other  end 

of  the  cylinder  is  escap- 
ing through  the  hollow 
interior  of  the  valve,  to 
the  exhaust  passage.  It 
then  escapes  to  the  air, 
or  to  the  condenser, 
through  a  pipe  at  the 
back,  which  does  not 
show  in  the  figure.  At 
the  end  of  the  stroke 
the  valve  is  pulled  far 
enough  to  the  right  to 
admit  live  steam  to  the 
left-hand  end  of  the 

cylinder,  while  the  spent  steam  in  the  right-hand  end  es- 
capes into  the  exhaust. 

In  large  steam  engines  Corliss  valves  are  more  often  used. 

A  Corliss  valve  (Fig.  186)  opens  and  closes  by  turning  a  little 

in  its  seat.     In  a  Corliss  engine  there  are  four  such  valves  — 

two  at  each  end  of  the  cylinder.     Two  of  them,  A  and  J5, 

are  for  admitting  the 

steam,    and    two,    O 

and  2>,  for  letting  the 

steam     out.       When 

valve  B   is    open  to 

admit  steam,  valve  D 

is    also    open   to    let 

steam  out  of  the  other 

end  of  the  cylinder, 

/  FIG.  186.  — Corliss  steam  engine. 

while   A  and    C  are 

closed  ;  on  the  reverse  stroke,  A  and  0  are  open,  while  B 
and  D  are  closed.  These  valves  are  automatically  opened 
and  closed  at  the  proper  time  by  the  engine  itself.  The  fact 


HEAT  ENGINES  225 

that  the  time  at  which  each  valve  opens  can  be  accurately 
adjusted  independently  of  the  other  valves  makes  Corliss 
engines  more  efficient  than  slide-valve  engines,  and  has  led 
to  their  extensive  use  in  large  installations. 

217.  Expanding  steam.     If  live  steam  from  the  boiler  is 
allowed  to  push  the  piston  through  its  entire  stroke,  and  is 
then  thrown  away,  that  is,  al- 
lowed to  pass  into  the  atmos- 
phere or  into  a  condenser,  it  is    T 

evident  that  much  energy  is 
wasted.  To  get  more  work  out 
of  the  steam,  the  valve  is  closed 
after  the  piston  has  made  about  siroke 

1    or    £   Of    its   Stroke,    and    the      FIG.  187.  -  Pressure  m  cylinder  of 
steam     is     allowed    to     expand 

through  the  rest  of  the  stroke.  The  pressure  continues  to 
drop  after  the  "  cut-off,"  as  shown  in  figure  187,  where  the 
pressure  P  is  represented  vertically  and  the  stroke  horizon- 
tally. Such  pressure  diagrams  can  be  made  automatically  by 
the  engine  itself  while  in  actual  operation,  and  enable  those 
in  charge  to  adjust  the  valves  properly. 

218.  Compound  engine.     Another  device  for  getting  more 
work  out  of  the  steam  is  to  use  the  steam  at  high  pressure 
in  one  cylinder,  then  allow  it  to  pass  into  a  second,  larger 
cylinder,  where  it  expands  some  more,  and  sometimes  into  a 
third  and  a  fourth  cylinder.     These  are  called  compound,  triple 
and   quadruple  expansion   engines.     When  the  expansion   and 
consequent  cooling  of  the  steam  take  place  in  steps,  there  is 
no  large  drop  in  temperature  in  any  one  cylinder.     So  the 
walls  of  a  cylinder  never  get  much  cooler  than  the  incoming 
steam,  and  there  is  little  condensation  in  the  cylinders.     In 
a  simple  engine,  the  initial  steam  pressure  varies  from  80  to 
100  pounds,  while  in  compound  engines  the  initial  pressure 
is  usually  higher,  from  100  to  175  pounds.     A  simple  engine 
requires  from   17  to  35  pounds  of  steam  an  hour  for  each 


226  PRACTICAL  PHYSICS 

horse  power  developed,  while  a  compound  engine  may  need 
as  little  as  11.2  pounds  of  steam  per  horse-power  hour. 
Triple-expansion  engines  are  usually  used  in  marine  work. 

219.  Condenser.     When  its   exhaust  pipe   opens  directly 
into   the   atmosphere,    an  engine   is    called   a   non-condensing 
engine.     The  power  depends  on  the   excess  of   the    steam 
pressure  in  the  boiler  above  that  of  the  atmosphere  outside. 
Ordinary  locomotives   and  most  small  engines  are  of   this 
type.     In  fact  the  locomotive  depends  on  the  escaping  steam 
to  furnish  a  draft  for  the  boiler. 

Greater  economy  is  obtained  by  sending  the  exhaust  steam 
to  a  vacuum  chamber,  or  condenser.  In  one  type  the  steam 
coming  from  the  engine  is  condensed  by  a  jet  of  cold  water, 
and  in  another  type  it  is  condensed  in  tubes  surrounded  by 
cold  water.  A  small  pump  is  used  to  pump  out  the  condensed 
steam  as  well  as  any  air  which  may  have  leaked  in.  Such 
engines  are  known  as  condensing  engines.  Marine  engines  are 
always  condensing  engines. 

220.  Efficiency  of  a  steam  plant.     We  have  already  seen 
that  the  modern  steam  boiler  has  an  efficiency  of  about  70%, 
but  there  are  still  larger  losses  in  the  engine  itself.     The 
escaping  steam  from  an  engine  always  carries  away  a  large 
amount  of  unutilized  heat  energy.     It  can  indeed  be  proved 
that  the  greatest  efficiency  possible  for  a  steam  engine  is 
represented  by  the  fraction 


where  T^  is  temperature  (Absolute)  of  the  steam  supplied 
and  Tz  is  temperature  (Absolute)  of  the  steam  rejected. 

For  example,  an  engine  running  at  163  pounds  boiler  pressure  takes  in 
steam  at  about  185°  C,  and  T^  is  458°.  If  the  temperature  of  the  exhaust 
steam  is  100°  C,  T2  is  373°.  Such  an  engine  cannot  possibly  have  an 
efficiency  greater  than 

468^-878 


HEAT  ENGINES  227 

For  this  reason  steam  engineers  try  to  use  high-pressure 
steam,  because  of  its  high  temperature,  so  as  to  make  (2\  —  T2) 
as  large  as  possible.  The  temperature  T^  is  sometimes  still 
further  increased  by  passing  the  steam  through  pipes  (Fig. 
183)  in  the  furnace  to  "  superheat "  it. 

It  must  be  remembered  that  this  18.5%  is  the  efficiency 
of  the  engine  alone,  so  that  the  efficiency  of  the  engine  and 
boiler  would  be  18.5  %  of  70  %,  or  only  about  13  %.  This 
means  that  about  87  %  of  the  energy  of  the  coal  would  not 
be  converted  into  mechanical  energy.  By  using  very  high 
temperatures,  the  latest  style  of  quadruple  expansion  and 
condensing  engine  has  been  made  to  utilize  about  20%  of 
the  energy  originally  in  the  coal.  The  ordinary  locomotive, 
however,  does  not  utilize  more  than  8  %. 

PROBLEMS 

1.  The  area  of  the  piston  of  a  steam  engine  is  120  square  inches  and 
its  stroke  is  2  feet.     If  the  "  mean  effective  pressure  "  of  the  steam  is  50 
pounds  per  square  inch,  what  is  the  total  force  exerted  on  the  piston  ? 

2.  In  problem  1,  how  many  foot  pounds  of  work  are  done  in  one 
revolution  of  the  shaft  (two  strokes)  ? 

3.  If  the  engine  in  problem  1  is  making  150  revolutions  per  minute, 
what  is  its  "  indicated  horse  power  " ;  that  is,  what  is  the  rate  in  H.  P.  at 
which  the  steam  does  work  on  the  piston  ? 

4.  A  locomotive  with  cylinders  18  inches  in  diameter  and  a  stroke  of 
2  feet  is  provided  with  driving  wheels  6  feet  in  diameter.     It  the  mean 
effective  pressure  of  the  steam  in  the  cylinder  is  60  pounds  per  square 
inch,  and  the  engine  is  making  50  miles  an  hour,  what  is  the  indicated 
horse  power  ? 

5.  How  much  mean  effective  steam  pressure  will  be  needed  to  get 
10  horse  power  from  a  "donkey  engine  "  running  at  200  revolutions  per 
minute  ?    (Assume  area  of  piston  to  be  50  square  inches,  and  stroke  1  foot.) 

221.  Steam  turbine.  Thus  far  we  have  been  describing 
reciprocating  engines,  in  which  the  back-and-forth  motion  of 
the  piston  rod  is  turned  into  rotary  motion  by  means  of  a 
crank  and  connecting  rod.  Since  the  piston  must  come  to  a 
standstill  at  the  end  of  each  stroke,  this  means  in  high- 


228 


PRACTICAL  PHYSICS 


speed  engines  very  frequent  starting  and  stopping,  which 
causes  so  much  shaking  as  to  require  big  and  expensive 
foundations.  On  steamships  the  continual  jarring  causes  a 
disagreeable  vibration.  A  new  and  distinctly  different 
type  of  engine  called  a  steam  turbine  has  been  developed 
in  recent  years  in  which  there  is  no  reciprocating  motion. 
222.  Curtis  turbine.  Steam  turbines  can  be  divided  into 
two  main  classes,  of  which  the  Parsons  and  the  Curtis  tur- 
bines are  typical  representatives. 
The  Curtis  turbine  is,  in  principle, 
like  the  Pelton  water  wheel  (sec- 
tions 78  and  79).  Steam  is  de- 
livered to  the  machine  through 
nozzles  in  which  it  expands  and 
gains  a  high  velocity.  It  then 
strikes  against  blades  fastened  to 
the  edge  of  a  revolving  disk  and 
gives  up  its  kinetic  energy  to 
them.  In  some  forms  of  turbine 
FIG.  188. -steam  turbine  with  one  ^ig.  188)  there  is  only  one  set 

set  of  nozzles.  J 

of  nozzles,  and  the  steam  expands 

in  one  step  from  the  boiler  pressure  to  the  condenser  vacuum. 
Under  such  conditions  the  speed  of  the  steam  as  it  strikes 
the  blades  is  so  great,  often 
more  than  4000  feet  per  second 
or  2700  miles  per  hour,  that 
it  is  difficult  to  handle  it  effi- 
ciently. Curtis  turbines  are 
therefore  built  in  from  three 
to  six  sections,  each  section  be- 
ing a  complete  turbine  with  its 
nozzles  and  wheel,  and  the  steam 
is  run  through  the  sections  in 
succession,  as  in  a  compound 

r.  FIG.  189.  —  Moving  and  stationary 

or  multiple-expansion  engine.  blades  in  a  Curtis  turbine, 


A  Curtis  turbine  (at  the  right)  with  the  upper  half  of  its  casing  removed. 
There  are  three  wheels  and  two  rows  of  blades  on  each  wheel.  It  is  used  to 
drive  the  generator  at  the  left. 


A  Westinghouse  turbine  with  the  upper  half  of  its  casing  lifted.  There  are  a 
great  many  rows  of  moving  blades.  The  balancing  dummies  are  at  the  near 
end.  The  generator  is  at  the  other  end,  and  is  cooled  by  air  drawn  in  through 
the  duct. 


" 


11 

ft-0 

s  -M 

o  o 
o 


sM 


1l! 


» 

rt    ^ 


3  s3 


2  2^ 


HEAT  ENGINES 


229 


In  order  to  reduce  still  further  the  speed  at  which  the 
blade  wheels  have  to  run,  they  are  so  designed  that  each  jet 
has  two  or  three  chances  at  a  given  blade  wheel  before  losing 
all  its  velocity.  As  it  escapes  at  reduced  speed  from  each 
set  of  moving  blades,  it  is  caught  by  guides  attached  to  the 
surrounding  casing  and  turned  around  so  as  to  strike  another 
set  of  moving  blades  on  the  same  wheel,  as  shown  in  figures 
189  and  190. 

223  Parsons  turbine.  The  Parsons  turbine  is  somewhat 
like  a  succession  of  windmills  set  in  line  behind  each  other. 
The  steam  flows  along  the  turbine  from  one  end  to  the  other 
in  the  annular  space  between  the  cylindrical  drum  or  rotor 
and  a  slightly  larger  cylindrical  casing,  and  acts  on  the  wind- 
mill-like blades  fastened  to  the  drum.  In  passing  through 
these  rows  of  moving  vanes,  the  steam  would  quickly  get  to 
spinning  with  the  rotor  and  would  then  fail  to  act  effectively 
on  the  later  vanes,  if  it  were  not  for  the  rows  of  stationary 
guide  blades  attached  to  the  casing.  These  project  between 
the  rows  of  moving  blades,  catch  the  steam  as  it  comes 
through,  and  direct  it  against  the  next  row  of  moving  blades 
at  the  proper  angle.  Thus  the  steam  goes  zigzagging  down 
the  annular  space,  striking  first  a  row  of  fixed  blades,  then  a 
row  of  moving  blades,  then 
another  row  of  fixed  blades, 
and  so  on.  As  the  steam 
flows  along,  its  pressure 
decreases  and  it  expands ; 
so  the  space  between  the 
rotor  or  drum  and  the 
outer  case  has  to  increase 
gradually  as  the  low-pressure  end  is  approached,  to  give  the 
steam  the  extra  space  it  requires.  This  is  done  by  making 
the  blades  short  at  the  inlet  end  and  long  at  the  outlet  end, 
and  by  occasionally  increasing  the  diameter  of  both  rotoi 
and  casing,  as  shown  in  figure  191. 


Ss/sncing  Dummies 


RotaHnybladts 

FIG.  191.  —  Section  of  a  Parsons  turbine. 


230  PRACTICAL  PHYSICS 

224.  Advantages    of    turbines.     Turbine   engines   always 
run  at  high  speed,  so  a  large  amount  of  power  can  be  de- 
livered by  a  small   machine.     This  makes   them  especially 
valuable  in  city  power   stations  where   land   is  •  expensive. 
Furthermore,  their  lightness  and  steadiness  make  smaller  and 
cheaper  foundations  sufficient.     They  have  been  installed  also 
on  large,  high-speed  passenger  vessels  and  on  torpedo  boats 
and  destroyers.     To  be  operated  most  efficiently  they  should 
work  through  a  wide  range  of  temperature,  corresponding  to 
a  boiler  pressure  of  from  200  to  250  pounds,  and  a  very  per- 
fect condenser  vacuum  (often  better  than  29  inches).     A 
large  supply  of  cool  condensing  water  is  therefore  desirable, 
and  turbines  are  especially  adapted  for  power  stations  on 
rivers,  lakes,  or  the  ocean.     Under  such  conditions,  when 
working  at  their  maximum  capacity,  they  are  slightly  more 
efficient  than  even  the  best  reciprocating  engines. 

225.  Gas    engine.     The    essential   difference    between   a 
steam  engine  and  a  gas  engine  is  that  in  the  steam  engine 
the  fuel  is  burned  under  a  boiler  and  the  working  substance, 
steam,  is  conducted  to  the  engine  in  pipes,  while  in  the  gas 
engine  the  fuel  is  burned  in  the  cylinder  of  the  engine  and 
the  hot  products  of  combustion  are  themselves  the  working 
substance.     In  othar  words,  the  gas  engine  is  an  internal  com- 
bustion engine.     The  fuel,  gasolene,  is  a  liquid  which  is  con- 
verted into  a  gas  in  what  is  called  a  carbureter.     The  liquid 
fuel  is  sprayed  into  the  carbureter,  vaporizes,  and  is  mixed 
with   the   proper   amount    of   air.       This    mixture   of   gas 
and  air  is  compressed  in  the  cylinder  of  the  engine  and  then 
exploded  by  an  electric  spark,  which  causes  the  exceedingly 
rapid  burning  of  the  gas.     This  results  in  an  enormous  in- 
crease in  pressure,  which  pushes  out  the  piston.     Then  the 
exploded  gases  are  forced  out  of  the  cylinder  and   a   new 
charge  of  gas  and  air  are  taken  in. 

Inasmuch  as  the  cylinder  has  to  be  a  furnace  as  well  as  a 
cylinder,  it  would  get  dangerously  hot  if  it  were  not  cooled 


HEAT  ENGINES 


231 


from  the  outside.  It  may  be  water-cooled  by  surrounding  it 
with  a  jacket  or  outer  case,  in  which  water  is  circulated  ;  or  it 
may  be  air-cooled  by  giving  it  a  corrugated  outer  surface 
which  radiates  heat  rapidly,  and  forcing  a  stream  of  air 
against  this  surface. 

226.  Two-cycle  engine.  In  the  two-cycle  gas  engine,  we 
have  one  explosion  for  every  two  strokes  or  for  each  revolution  of 
the  crank  shaft.  A  simple  form,  such  as  is  used  on  motor 
boats,  is  shown  in  figure 
192.  The  explosive  mix- 
ture is  taken  into  an  air- 
tight crank  case  and 
slightly  compressed  on 
the  outward  or  down 
stroke  of  the  piston.  As 
the  piston  nears  the  bot- 
tom of  its  stroke,  it  un- 
covers first  the  outlet  port, 
E,  letting  part  of  the 
spent  gases  in  the  cylin- 
der blow  off,  and  then 
the  inlet  port  B.  The  slightly  compressed  charge  in  the  crank 
case  then  rushes  into  the  cylinder,  sweeping  out  the  rest  of 
the  exploded  gases  before  it.  On  the  upstroke  of  the  piston 
the  ports  are  covered  and  the  fresh  charge  is  considerably 
compressed.  As  the  piston  passes  its  upper  dead  center 
(or  soon  afterward)  the  charge  is  exploded,  and  expands  at 
a  much  higher  average  pressure  than  during  the  compres- 
sion, giving  back  the  work  of  compression  and  considerably 
more  besides.  Such  an  engine  is  called  single  acting,  meaning 
that  work  is  done  only  on  one  side  of  the  piston. 

If  the  spark  does  not  come  at  the  upper  dead  center,  but 
part  way  down  the  expansion  stroke,  the  power  yielded  is  much 
less.  This  is  done  to  make  a  boat  run  slowly.  Adjusting 
the  electrical  connections  so  as  to  bring  the  time  of  explosion 


FIG.  192.  — Two-cycle  engine. 


232 


PRACTICAL   PHYSICS 


(1) 


nearer  the  upper  dead  center  is  called  "  advancing  the  spark." 
Running  on  a  "  retarded  spark  "  wastes  gasolene,  because  the 
amount  used  per  stroke  is  the  same  as  at  full  power. 

The  only  true  valve  in  this  engine  is  a  light  clap  valve, 
where  the  fresh  gases  enter  the  crank  case. 

The  disadvantage  of  this  style  of  engine  is  that  some  of  the 
fresh  gas  is  lost  with  the  spent  gases  through  the  exhaust,  so 
that  it  uses  more  gasolene  than  some  other  styles.  But,  on  the 
other  hand,  it  is  very  simple  and  gives  a  push  every  revolution. 
227.  Four-cycle  engine.  In  the  four-cycle  engine,  we  get 
a  push  or  thrust  only  once  in  every  two  revolutions  or  every 
four  strokes  of  the  piston.  Four-cycle  engines,  like  two-cycle 
engines,  are  usually  single  acting. 

The  four-cycle  type  is  the  one  most  commonly  used  for 
automobiles  and  for  stationary  work.     The  four  strokes  of 

the  piston,  corresponding  to 
two  revolutions  of  the  shaft,  are 
shown  in  figure  193.  It  will  be 
noticed  that  whereas  the  two- 
cycle  type  has  no  valves  in  the 
cylinder,  the  four-cycle  has  two 
valves,  one  for  the  intake  of  gas 
and  air  and  another  for  the  ex- 
haust of  the  spent  gases.  These 
valves  are  operated  mechani- 
cally by  cams  on  a  small  half-time  shaft,  which  is  driven 
through  gears  at  half  the  speed  of  the  main  shaft.  In  figure 
193,  (1),  the  intake  valve  is  open,  and  the  piston  is  going  down, 
thus  drawing  in  the  explosive  mixture.  In  (2)  the  return 
or  back  stroke  of  the  piston  compresses  the  mixture.  In  (3) 
the  mixture  has  been  ignited  by  an  electric  spark  or  flame, 
and  power  is  obtained  from  the  thrust  of  the  expanding  gas 
on  the  outward  stroke.  This  is  the  working  stroke.  In  (4) 
the  exhaust  valve  is  open  and  the  spent  gases  are  being 
pushed  out  of  the  cylinder  by  the  returning  piston.  Then 


FIG.  193.  —  Four  cycles  of  a  gas 
engine. 


HEAT  ENGINES  233 

the  whole  cycle  is  repeated  again.  Since  power  is  obtained 
only  on  every  alternate  outward  stroke,  a  heavy  flywheel  is 
used  to  keep  the  engine  going  during  the  other  three  strokes, 
or,  as  in  automobiles,  four  such  engines  may  act  on  the  same 
shaft,  so  arranged  that  the  explosions  in  the  several  cylinders 
take  place  successively,  one  for  every  half  revolution  of  the 
shaft. 

228.  Disadvantages  of  the  gas  engine.    Although  the  internal 
combustion  engine  has  been  immensely  improved  in  the  last 
decade,  it  is  still  a  very  sensitive  machine.     The  spark  must 
come  at  just  the  right  time,  and  must  come  every  time.     The 
method  for  producing  the  spark  will  be  described  in  Chapter 
XVII.     The  steam  engine  is  more  easily  varied  in  speed  than 
the  gas  engine.     To  be  sure,  it  is  possible  to  vary  the  speed  of  a 
gas  engine  somewhat  by  advancing  or  retarding  the  spark,  and 
by  controlling  the  supply  of  gas  ;  nevertheless,  automobiles 
have  to  use  gears  to  get  a  sufficient  variety  of  speeds  at  full 
power.     Then,  too,  a  steam  locomotive  will  run  either  way 
by  simply  shifting  the  slide  valve,  while  the  gasolene  auto- 
mobile has  to  use  a  reversing  gear.     Finally  a  gas  engine  is 
not  always  free  from  noise  and  smell. 

229.  Advantages  of  the  gas  engine.     On  account  of  light- 
ness and  compactness,  and  the  small  space  occupied  by  the 
fuel,  there  has  been  a  phenomenal  development  in  the  manu- 
facture of  gasolene  engines  for  small  pumping  stations,  shops, 
and  factories,  as  well  as  for  automobiles,  launches,  and  ae'ro- 
planes.     The  gas  engine  does  not  require  any  stoking  of  a 
boiler  or  constant   care    to  keep  up   the  right  pressure  of 
steam.     In  fact,  once  started  it  requires  very  little  attention. 
It  can  be  started  at  a  moment's  notice,  while  if   a   steam 
engine  and  its  boiler  have  been  "  shut  down,"  it  takes  a  good 
while  to  get  up  steam.       Furthermore,  no  fuel  is  wasted 
when  a  gas  engine  is  shut  down  at  night  or  between  periods 
of  use.     In  efficiency  the    modern  gas  engine  ranks  much 
higher  than  the  steam  engine. 


234 


PRACTICAL  PHYSICS 


230.  Balance  sheet  of  heat  engines.  When  an  engine  is 
tested,  a  heat  balance  sheet  is  usually  made  up.  This  is 
somewhat  like  a  cash  account,  in  that  it  accounts  for  all  the 
energy  delivered  to  the  engine  by  the  fuel.  These  heat  bal- 
ance sheets  vary  somewhat  for  different  engines  even  of 
good  design,  but  the  following  are  fairly  typical  for  large 
and  efficient  engines  of  the  two  types  :  — 


STEAM  ENGINE 

Useful  work  15% 

Friction  5  % 

Exhaust  45  % 

Up  the  chimney     35% 
100% 


GAS  ENGINE 

Useful  work 
Friction,  etc. 
Exhaust 
Jacket 


25% 

10% 

30% 

35% 

100% 


231.  Mechanical  equivalent  of  heat.  We  have  been  con- 
sidering the  efficiency  of  engines  without  stopping  to  de- 
scribe how  it  is  measured.  Evidently  we  must  have  some 
way  of  comparing  the  output,  which  would  naturally  be 
measured  in  foot  pounds  or  kilogram  meters,  with  the  input, 
which  would  naturally  be  measured  in  B.  t.  u.  or  calories. 
This  involves  finding  a  definite  relation  between  a  foot 
pound  and  a  B.  t.  u.,  or  between  a  kilogram  meter  and  a 

calorie.  This  problem  was 
not  solved  until  about  the 
middle  of  the  last  century, 
when  an  Englishman,  Joule 
(1818-1889),  did  his  famous 
experiment  of  churning 
water. 

He     arranged     a    paddle 
wheel   in    a    box    of    water 

FIG.  194.— Joule's  machine  to  find  me-      (Fig.     194).        The     paddles 
chanical  equivalent  of  heat.  were       ^^      ^y      weights 

which  descended  and  thus  unwound  cords  on  the  spindle 
of  the  wheel.     The  water  was  kept  from  following  the  rotat- 


HEAT  ENGINES  235 

ing  paddles  by  fixed  paddles  which  projected  from  the  sides 
of  the  box. 

In  this  experiment  the  mechanical  work  put  in  could  be 
measured  by  multiplying  the  weights  by  the  distance  through 
which  they  fell ;  and  the  heat  produced  could  be  measured 
by  multiplying  the  weight  of  the  water  by  the  rise  in  tem- 
perature. Great  care  was  taken  to  prevent  any  loss  of  heat. 
The  result  of  this  and  many  other  experiments  of  a  similar 
nature  led  Joule  to  announce  this  principle:  The  number  of 
units  of  work  put  in  is  always  proportional  to  the  number  of 
units  of  heat  produced. 

As  a  result  of  Joule's  experiments  and  also  of  the  more 
accurate  experiments  of  Rowland  (1848-1901)  and  of  many 
others,  we  believe  that  778  foot  pounds  of  work  are  equivalent 
to  the  heat  required  to  raise  one  pound  of  water  one  degree 
Fahrenheit,  or  that  the  energy  required  to  heat  one  kilogram  of 
water  one  degree  Centigrade  is  equal  to  the  work  done  in  rais- 
ing one  kilogram  to  a  height  of  427  meters. 

1  B.  t.  u.  =  778  foot  pounds  of  work. 
1  kilogram  calorie  =  427  kilogram  meters  of  work. 

To  compute  the  efficiency  of  an  engine  we  have,  therefore, 
to  divide  the  work  done  by  the  heat  put  in,  expressing  both 
in  the  same  units  by  means  of  the  above  relationships. 

This  work  of  Joule's  was  a  clinching  argument  in  favor  of 
the  principle  of  the  conservation  of  energy,  for  it  meant  that 
heat  and  work  are  but  different  forms  of  energy. 

PROBLEMS 

1.  If  a  horse  power  is  equal  to  33,000  foot  pounds  of  work  per  minute, 
how  many  foot  pounds  are  there  in  a  horse  power  hour;  that  is,  in  the 
total  amount  of  work  produced  by  a  1  H.  P.  engine  working  for  1  hour? 

2.  A  pound  of  average  coal  yields  14,500  B.  t.u.  when  burned.     To 
how  many  foot  pounds  is  this  heat  equivalent  ? 

3.  From  the  results  of  problems  1  and  2,  calculate  the  horse  power 
hours  per  pound  of  coal. 


236  PRACTICAL   PHYSICS 

4.  A  test  of  a  certain  steam  engine  showed  that  1  pound  of  coal 
generated  1  horse  power  hour;  from  the  three  preceding  problems  com- 
pute the  efficiency. 

5.  Calculate  the  efficiency  of  a  gasolene  engine  from  the  following 
data:     16  cubic  feet  of  gas  were  used  per  horsepower  hour;    1  cubic 
foot  of  gas  yields  700  JB.  t.  u. 


SUMMARY   OF  PRINCIPLES   IN   CHAPTER  XII 

The  mechanical  equivalent  of  heat  is  the  value  in  foot  pounds 
of  one  B.  t.  u.  or  in  kilogram  meters  of  one  calorie. 

1  B.  t.  u.   =  778  ft.  Ib. 

1  kg.  cal.  =  427  kg.  meters. 

Efficiency  =  2^'. 
input 

Both  must  be  expressed  in  same  unit  by  means  of  above 
relations. 

The  conservation  of  energy  in  engines  requires  that  all 
energy  supplied  as  heat  of  combustion  of  the  fuel  be  accounted 
for  as  useful  output  or  specified  waste  ("making  up  the  heat 
balance  sheet  of  the  engine  "). 

QUESTIONS 

1.  Why  does  the  steam  jacket  increase  tne  efficiency  of  a   steam 
engine  ? 

2.  Does  the  water  jacket  increase  the  efficiency  of  a  gasolene  engine? 

3.  What  did  Count  Rumford  learn  about  heat  while  boring  cannon 
for  the  Bavarian  government? 

4.  How  are  the  cylinders  of  engines  lubricated? 

5.  How  does  a  ship  equipped  with  steam  turbines  reverse  its  pro- 
pellers?* 

6.  Describe  the  reversing  mechanism  of  a  locomotive. 

7.  Is   an   ordinary  gas   engine  self-starting?     How  are   automobile 
engines  made  self-starting? 

8.  When  you  see  steam  coming  from  the  exhaust  pipe  of  a  steam 
engine  in  puffs,  do  you  know  whether  it  is  a  condensing  or  non-condens- 
ing engine  ? 

9.  Why  are  condensers  not  used  on  locomotives? 


HEAT  ENGINES  237 

10.  What  advantages  has  oil  as  a  fuel  for  locomotives  and  steam- 
ships ? 

11.  Why  are  marine  engines  always  condensing  engines? 

12.  How  would  you  compute  the  efficiency  of  a  gun  regarded  as  a 
heat  engine  ? 

13.  What  makes  the  water  circulate  in  a  water-tube  boiler? 

14.  Why  does  a  high-speed  turbine  give  more  power  than  a  low= 
speed  reciprocating  engine  of  about  the  same  size  ? 

15.  What  is  the  use  of  the  radiator  on  an  automobile  ? 


CHAPTER   XIII 

MAGNETISM 

The  lodestone  —  magnetic  poles  —  attraction  and  repulsion 
—  the  compass  and  magnetism  of  the  earth  —  magnetic  field  — 
induced  magnetism  —  permeability  —  theory  of  magnetism. 

232.  The   lodestone.      For    many   centuries    it    has    been 
known  that  a  certain  kind  of  rock,  called  the  lodestone,  has 
the  power  of  attracting  iron  filings  and  small  fragments  of 
the  same  rock.     Its  abundance  near  Magnesia  in  Asia  Minor 

led   the    Greeks   to   call   it    "  magnetite "    or 
"  magnetic  "  iron  ore. 

Let  us  take  a  piece  of  magnetite  (Fe3O4)  and  show 
that  it  picks  up  pieces  of  iron  (Fig.  195),  but  does  not 
pick  up  copper  or  zinc.  We  may  magnetize  a  knitting 
needle  by  stroking  it  with  a  piece  of  magnetite. 

This  kind  of  iron  ore  occurs  in  many  places 
in   this  country   as   well   as   in    Norway  and 
FIG.  195.  —  Lode-   Sweden.     When   a  steel   bar  is  rubbed    with 
stone   attracts   such  a  natural  magnet,  the  steel  itself  becomes 
magnetic  and  is  then  called  an  artificial  mag- 
net.    In  a  later  chapter  we  shall  learn  how  to  make  magnets 
by  using  an  electric  current. 

233.  Magnetic  poles.     It  was  a  good  many  years  before 
any  one  in  Europe  noticed  that  the  magnetic  proper.ty  of  a 
lodestone  was  concentrated  more  or  less  definitely  in  two  or 
more  spots,  and  that  if  a  somewhat  elongated  lodestone  with 
only  two  of  these  spots,  and  those  near  its  ends,  is  hung  by 
a  thread,  it  will  set  itself  with  one  spot  toward  the  north 
and  the  other  toward  the  south.     We  now  use  magnetized 

238 


MAGNETISM  239 

needles  instead  of  lodes  tones,  and  call  such  an  arrangement 
a  compass,  and  we  all  know  how  valuable  it  is  to  mariners 
and  explorers.  Probably  the  Chinese  had  compasses  many 
years  before  Europeans  reinvented  them. 

The  two  spots  which  point  one  to  the  north  and  one  to 
the  south  are  called  the  poles  of  the  magnet ;  one  is  called 
the  north-seeking  pole  (N)  and  the  other  the  south-seeking 
pole  (#). 

234.    Magnetic   repulsion.      It  was   many  centuries   after 
people  had  known  that  magnets  would  at- 
tract things  before  they  learned  that  mag- 
nets sometimes  repel  things. 


If  we   bring  the  north-seeking  or  JV-pole  of  a 
magnet  near  the  ^V-pole  of  a  suspended  magnet,  the 
poles  repel  each  other  (Fig.  196).     If  we  bring  the 
two   S-poles  together,   they   also   repel  each  other.    FIG.   1^96.  —  Magnetic 
But  if  we  bring  an  N-po\e  toward  the  S-pole  of  the  repulsion, 

moving  magnet,  or  an  S-pole  to  the   jV-pole,  they  attract  each  other. 

That  is, 

Like  poles  repel  each  other, 
Unlike  poles  attract  each  other. 

Experiment  shows  that  these  attractive  or  repulsive  forces 
vary  inversely  as  the  square  of  the  distance  between  the 
poles. 

235.  Declination  and  dip.  Soon  after  the  compass  was 
invented,  it  was  noticed  that  it  did  not  point  true  north 
and  south.  For  a  long  time  it  was  supposed  that  this  de- 
viation or  declination  was  everywhere  the  same,  until  Colum- 
bus, on  his  way  to  America  in  1492,  discovered  near  the  Azores 
a  place  of  no  declination.  Evidently  an  exact  knowledge  of 
the  declination  at  different  places  is  of  the  greatest  impor- 
tance to  mariners  and  surveyors,  and  so  careful  maps  are 
published  by  the  different  governments  giving  lines  of  equal 
declination.  Figure  197  shows  such  a  map.  From  this  map 
it  will  be  observed  that  in  the  extreme  eastern  section  of  the 


240 


PRACTICAL  PHYSICS 


United  States  the  declination  is  as  much  as  20°  W.  This 
decreases  to  zero  at  a  place  near  Cincinnati,  O.,  and  becomes 
an  easterly  declination  amounting  to  20°  E.  in  the  northwest. 


FIG.  197.  —  Map  showing  declination  of  the  compass  in  the  United  States. 

It  was  nearly  a  hundred  years  after  Columbus'  time  before 
it  was  discovered  that  if  a  compass  needle  is 
perfectly  balanced  so  that  it  can  swing  up  and 
down  as  well  as  sidewise,  its  north-seeking  pole 
will  dip  down  at  a  considerable  angle  (Fig/ 
198).  This  angle  increases  as  one  goes  farther 
north,  and  decreases  as  one  goes  south.  Along 
a  line  near  the  equator  there  is  no  dip.  In 
the  southern  hemisphere  the  north-seeking 
pole  of  a  needle  points  up  in  the  air,  and  re- 
cently Shackleton's  South  Polar  Expedition 
FJG.  198.  —  Com-  found  a  point  on  the  great  Antarctic  conti- 
pass  needle  to  nent  w^ere  a  neecQe  would  hang  vertically 

show     magnetic        .  ,    .,  ,  -,  .  -, 

dip  with  its  north-seeking  pole  on  top. 


MAGNETISM  241 

236.  The  earth  a  magnet.  An  Englishman,  Gilbert,  in 
the  sixteenth  century  was  the  first  to  explain  these  curious 
magnetic  phenomena.  He  had  ground  a  little  lodestone  into 
the  shape  of  a  globe,  and  noticed  that  when  tiny  compass 
needles  were  brought  near  it,  they  acted  just, 
like  compasses  on  the  surface  of  the  earth. 
So  he  called  his  lodestone  globe  the  "ter- 
rella  "  or  "  little  earth  "  (Fig.  199),  and  came 
to  believe  that  it  gave  a  true  representation 
of  the  earth  itself. 

The  earth  is,  then,  simply  a  huge  magnet, 
much  thicker  in  proportion  to  its  length  than  FlG  199  _Qiibert's 
the  magnets  with  which  we  are  familiar  in  labo-  terreiia  or  little 
ratories,  but  otherwise  exactly  like  them.  earth- 
It  has  a  north-seeking  and  a  south-seeking  pole  like  any  other 
magnet,  but  from  the  laws  of  attraction  and  repulsion  we  see 
that,  curiously  enough,  its  south-seeking  pole  must  be  at 
Peary's  end,  and  its  north-seeking  pole  at  Amundsen's  end. 
These  magnetic  poles  are  not  exactly  at  the  geographical 
poles.  One  of  them  is  in  North  America  near  Hudson's  Bay 
and  the  other  is  nearly  opposite. 

Since  the  lines  of  equal  declination  and  of  equal  dip  are 
not  true  circles,  the  magnetization  of  the  earth  must  be 
somewhat  irregular.  Furthermore,  the  positions  of  its  mag- 
netic poles  are  known  to  be  changing  slowly  from  year  to 
year.  Why  these  things  are  so,  and,  for  that  matter,  why 
the  earth  is  magnetized  at  all,  is  not  yet  known. 

QUESTIONS 

1.  Does  a  magnet  ever  have  more  than  two  poles  ? 

2.  In  what  direction  did  Peary's  compass  point  when  he  reached  the 
North  pole  ? 

3.  How  far  is  the  magnetic  pole  from  the  geographical  North  pole  ? 

4.  How  can  you  tell  whether   or  not  a   steel   rod   is  a  permanent 
magnet  ? 

5.  Why  are  knives,  files,  and  scissors  sometimes  found  to  be  magnetized? 


242 


PRACTICAL   PHYSICS 


6.  Will  a  magnet  attract  a  tin  can  ?     Explain. 

7.  Would  a -magnet  floating  on  a  cork  in  a  dish  of  water  float  toward 
the  north,  as  well  as  turn  north  and  south  ? 

8.  What  advantage  is  there  in  making  a  magnet  in  the  shape  of  a 
horseshoe  ? 

237.  The  field  around  a  magnet.  Michael  Faraday  (1791- 
1867)  was  the  first  to  see  that  a  true  understanding  of  the 
action  of  magnets  could  be  had  only  by  studying  the  empty 
space  around  them,  as  well  as  the  magnets  themselves. 

One  way  to  do  this  is  to  lay  a  stiff  piece  of  paper  over  a  magnet  and 
sprinkle  iron  filings  on  it  (Fig.  200).  When  the  paper  is  tapped  lightly 
so  as  to  shake  the  filings  about  a  little,  they  arrange  themselves  in 
regular  lines  leading  from  one  pole  to  the  other.  This  is  because  each 


Fia.  200.  —  Magnetic  lines  of  force  around  a  bar  magnet. 

filing  gets  slightly  magnetized  by  the  influence  of  the  original  magnet, 
and  sets  itself  in  the  direction  in  which  a  tiny  compass  needle  would 
lie  if  it  were  at  the  same  place.  This  can  be  verified  by  actually  using 
a  small  compass  instead  of  the  filings.  The  lines  can  be  mapped  in  this 
way,  but  it  is  not  as  quickly  done. 

In  this  way,  Faraday  drew  what  he    called   lines  of  force 
around  a  magnet.     A  line  of  force  may  be  defined  as  a  line 


MAGNETISM  243 

which  indicates  at  its  every  point  the  direction  in  which  a 
north- seeking  pole  is  urged  by  the  attractions  and  repul- 
sions of  all  the  poles  in  the  neighborhood.  When  lines 
of  force  are  thought  of  in  this  way,  they  should  have  little 
arrowheads  on  them,  pointing  in  the  direction  of  their 
journey  from  a  north-seeking  pole  to  a  south-seeking  pole. 
We  shall  find  this  conception  of  lines  of  magnetic  force  or 
magnetic  flux  a  convenient  way  of  remembering  how  a  magnet 
will  affect  other  magnets  in  its  vicinity. 

238.  Lines  of  force  like  elastic  fibers.  Faraday  himself 
thought  of  these  lines  of  force  as  having  a  much  more  real 
meaning  than  this.  He  thought  of  them  as  actually  existing 
throughout  the  space  around  every  magnet,  even  when  there 
are  no  filings  to  show  them.  He  believed  that  they  repre- 
sent a  real  state  of  strain  in  the  ether  (see  section  187),  in 
which  all  material  bodies  are  immersed.  Even  now  we 
know  very  little  about  what  the  ether  really  is.  We  know 
simply  that  it  is  not  a  kind  of  matter,  but  something  much 
more  subtle  and  fundamental. 

At  any  rate,  these  lines  of  force  of  Faraday's  act  as 
if  they  were  stretched  fibers  in  the  ether  which  are  con- 
tinually trying  to  contract  and  are  thus  pulling  on  the 
poles  at  their  ends.  They  also  act  as  if  they  were  trying 
to  swell  up  sidewise  as 
they  contract,  and  thus 

seem  to  crowd  each  other      *x       \     /  ^'"""^^   \    / 
apart.     It  is  not  easy  to     -~~-^Xs 
see  why  lines  of    force     -—--_:--_;: 
have    these    properties,      C...  (*„ 

but  once  the  properties  7^::-i--        '>V:: 

are  assumed  (as  rules  of        "  ,.-''   >  \\^'       '''/'I  \    \  ~~~ 
the  game),  it  is  easy  to      ***        /     \    ^—          /     \ 
reason    out    from   them  /         \ 

what  will  happen  in  many 

.  FIG.  201.  — Lines  of  force  between  two  unlike 

practical  cases.  poles> 


244 


PRACTICAL   PHYSICS 


For  example,  if  two  magnets  are  placed  with  their  unlike  poles  to- 
gether and  their  lines  of  force  traced  with  iron  filings,  the  result  will  be  as 

shown  in  figure  201.     If  we 

\  /          »N  •  ,        assume  that  the  lines  of  force 

/  \          i  /         tend  to  contract,  it  is  easy  to 

poles 
Like 


FIG.  202. — Lines  of  force  between  two  like  poles. 

an  easy  way  of  seeing  what  will  happen,  and  it  will  be  useful  later  on 


see  that  two  unlike 
must  attract  each  other, 
poles,  however,  would  show 
a  field  of  force  as  shown  in 
figure  202,  and  if  we  assume 
that  lines  of  force  squeeze 
against  each  other  sidewise, 
and  tend  to  separate,  evi- 
dently two  like  poles  must 
repel  each  other.  This  is  not 
an  explanation  of  why  these 
things  happen ;  it  is,  however, 


239.  Induced  magnetism.  If  we  plunge  one  end  of  a  piece  of 
unmagnetized  soft  iron  into  some  iron  filings,  it  does  not  attract  them, 
but  if  we  bring  near  it  a  permanent  magnet,  as 
shown  in  figure  203,  the  soft  iron  becomes  a 
magnet  and  attracts  the  filings.  When  the  per- 
manent magnet  is  removed,  the  soft  iron  loses  its 
magnetism,  and  drops  the  filings. 

A  piece  of  iron  which  is  magnetized  by 
being  near  a  magnet  is  said  to  be  magnet- 
ized by  induction.  If  the  pole  of  the  mag- 
net, which  was  brought  near  the  iron,  was 
a  north-seeking  pole,  the  induced  magnet 
can  be  shown  by  a  compass  to  have  a 
^V-pole  away  from  the  magnet  and  a  $-pole 
near  the  magnet. 

Experiments  show  that  very  soft  iron 
quickly  becomes  magnetized  by  induction  FlG 
and  quickly  loses  its  magnetism  when  re- 
moved from  the  field.     Hardened  steel,  however,  is  magnet- 
ized with  difficulty,   but  retains  its  magnetism  well.     For 


MAGNETISM 


245 


this  reason  the  magnets  used  in  telephones  and  magnetos  are 
made  of  hardened  steel. 

240.  Permeability.  Although  a  magnet  will  act  through 
a  vacuum  or  through  glass  or  wood,  yet  the  magnetic  flux 
seems  to  prefer  soft  iron  to  any  other  medium. 

We  can  show  this  by  the  following  experiment.  We  will  take  a 
horseshoe  magnet  and  lay  across  its  poles  a  sheet  of  stiff  paper,  and  then 
bring  up  a  mass  of  iron  filings  under  the  paper.  The  iron  filings  will 
cling  under  the  poles  as  shown  in  figure  204.  If  we  slip  a  plate  of  glass 
between  the  paper  and  the  poles  at  A  A,  most  of 
the  filings  still  stick,  but  when  we  substitute  an 
iron  plate  for  the  glass,  most  of  the  filings  drop 
off  immediately.  This  shows  that  an  iron  plate 
screens  the  region  beyond  from  the  magnetic 
action. 


FIG.  204.  —  iron  is  more 
Permeable  than 


Lord  Kelvin  has  called  the  ease  with 
which  lines  of  force  may  be  established 
in  any  medium  as  compared  with  a- 
vacuum,  the  permeability  of  the  medium.  Thus  iron  has  a 
permeability  several  hundred  times  greater  than  air.  When 
a  watch  is  brought  near  a  powerful  magnet,  its  balance 
wheel  is  often  magnetized.  This  disturbs  its  working.  To 
protect  it  from  such  magnetic  disturbances  a  good  watch  is 
often  inclosed  in  a  soft  iron  case. 

241.  Theory  of  magnetism.  Our  present  theory  of  magnet- 
ism was  suggested  by  the  following  experiment. 

Let  us  harden  a  knitting  needle  or  a  piece  of  watch  spring  by  first 
heating  it  red  hot,  and  then  plunging  it  into  cold  water.  Then  let  us 
magnetize  it  and  mark  the  AT-pole.  If  we  now  break  it  near  the  middle 


Fia.  205.  —  A  broken  magnet  shows  poles  at  the  break. 

where  it  does  not  show  any  magnetism,  we  shall  find,  by  bringing  the 
broken  ends  near  a  compass  needle,  that  we  have  an  ^V-pole  arid  an 
S-pole  as  indicated  in  figure  205.  If  we  repeat  the  process,  we  shall 


246  PRACTICAL  PHYSICS 

find  that   each   time   the  magnet   is   broken,  new  poles  are  formed  at 
the  break. 

A   magnet  can  be  broken  into  a  great  number  of  little 
magnets.     A  glass  tube  full  of  iron  filings  can  be  magnetized, 
but   when   shaken,  it   loses  its  magnetism.      Any  magnet 
loses  a  part  or  all  of  its  power  if  it  is  heated  red  hot,  jarred, 
hammered,  or  twisted. 

All   these    facts    point  to  a  molecular  theory  of  magnetism, 
which  was  suggested  by  a  Frenchman,  Ampere,  and  elaborated 
by  a  German,  Weber,  and  an  Englishman,  Ewing.     Every 
molecule  of  a  bar  of  iron  is  supposed  to  be  itself  a  tiny 
permanent  magnet  —  why,  no  one  yet  knows.      Ordinarily, 
________________________    these    molecular    magnets 

are  turned  helter-skelter 
throughout  the  bar  (Fig. 
206),  and  have  no  cumu- 

FIG.  206.  —  Unmagnetized  bar.  lative    effect    that    can    be 

noticed  outside  the  bar.  When  the  bar  is  magnetized,  how- 
ever, they  get  lined  up  more  or  less  parallel  (Fig.  207), 
like  soldiers,  all  facing  the  same  way.  Near  the  middle  of 
the  bar  the  front  ends  of  one  row  are  neutralized  by  the 
back  ends  of  the  row  in  front;  but  at  the  ends  of  the  bar  a 
lot  of  unneutralized  poles 
are  exposed,  north-seeking 
at  one  end  and  south-seek- 
ing at  the  other.  These 

..   c  , ,  FIG.  207.  —  Magnetized  bar. 

free  poles  make  up  the  ac- 
tive spots  which  we  have  called  the  poles  of  the  magnet. 

On  this  theory  it  is  easy  to  see  that  when  a  magnet  is 
broken  in  two  without  disturbing  the  alignment  of  the 
molecular  magnets,  the  new  poles  which  appear  at  the  break 
are  simply  collections  of  molecular  poles  that  have  been 
there  all  the  time,  but  are  now  for  the  first  time  in  an 
independent,  recognizable  position. 

It  will  also  be  evident  that,  if  this  theory  is  true,  there 


cmcmcmca 


MAGNETISM  247 

is  a  perfectly  definite  limit  to  the  amount  of  magnetism  a 
given  piece  of  iron  can  have.  For  when  all  the  molecular 
magnets  are  lined  up  in  perfect  order,  there  is  nothing  more 
that  can  be  done,  no  matter  how  strong  the  magnetizing 
force  may  be.  Such  a  magnet  is  said  to  be  saturated. 

SUMMARY   OF   PRINCIPLES   IN   CHAPTER   XIII 

Like  poles  repel  each  other. 

Unlike  poles  attract  each  other. 

The  earth  is  a  magnet  with  its  "  south-seeking  "  pole  at  Peary's 
end. 

Lines  of  force  tend  to  contract  and  swell  sidewise ;  that  is,  there 
is  tension  along  them,  and  compression  at  right  angles  to  them. 

QUESTIONS 

1.  If  two  bar  magnets  are  to  be  kept  side  by   side  in  a  box,  how 
should  they  be  arranged  ?     Why  ? 

2.  If  a  magnetic  needle  is  attracted  by   a  certain   body,   does  that 
prove  that  the  body  is  a  permanent  magnet? 

3.  What  is  meant  by  the  "  aging  "  of  magnets  ? 

4.  How  must  a  ship's  compass  box  be  supported   so   as  to  remain 
steady  during  the  rolling  of  the  ship  ? 

5.  A  long  soft  iron  bar  is  standing  upright.     Why  does  its  lower  end 
repel  the  north  pole  of  a  compass  needle  ? 

6.  Does  hammering  the  bar  while  it  is  in  the  position  described  in 
problem  5  increase  or  decrease  the  effect  ?     Why  ? 

7.  Why  are  the  hulls  of  most  iron  ships  permanently  magnetized? 
What  determines  the  direction  in  which  they  are  magnetized? 

8.  How  can  the  compass  on  an  iron  ship  be  "  compensated  "  for  the 
induced  magnetism  in  the  ship? 

9.  The  Carnegie  Institute  has  a  special  ship  built   almost  without 
iron.     What  kind  of  a  survey  of  the  world  do  you  suppose  it  is  made 
for  ?     What  is  the  advantage  of  such  a  ship  for  this  purpose  ? 

10.  How  does  a  jeweler  demagnetize  a  watch? 

11.  What  effect  does  the  angle  of  dip  have  on  the  horizontal  intensity 
of  the  earth's  magnetism  at  any  point  ? 


CHAPTER   XIY 

THE   BEGINNINGS   OF   ELECTRICITY 

Frictional  electricity —  conductors  and  insulators  —  positive 
and  negative  charges  —  electroscope  —  frictional  electric  machine 

—  the  lightning  rod  —  induction  —  Leyden  jar  —  electrophorus 

—  theories  as  to  nature  of  electricity. 

242.  Electricity  by  friction.     As   far  back   as  600  B.C., 
Thales  of  Miletus,  one  of  the  "  seven  wise  men,"  knew  that 
the  yellow  resinous  substance  called  amber,  of  which  pipe- 
stems  and  jewelry  are  now  often  made,  would,  when  rubbed, 
attract  bits  of  paper  or  other  light  objects.     We  now  know 
that  many  other  substances,  such  as  rubber,   glass,  and  sul- 
phur, have  the  same  property.     Any  one  can  observe  this  on 
a  cold,  dry  morning  after  combing  his  hair  vigorously  with  a 
hard  rubber  comb.     The  comb  will  then  support  long  chains 
of  bits  of  paper.     Another  way  to  show  this  is  to  scuff  one's 
feet  on  a  carpet,  or  to  rub  a  cat's  back.     In  either  case,  if 
the    knuckle   is    brought   near   a   gas   fixture,    tiny   sparks 
will  pass.     Since  amber,  in  common  with  gold  and  certain 
bright  alloys,  was  called  "  electron,"  by  the  Greeks,  these 
phenomena    were    many    years     later    named    by    Gilbert 
"  electric,"  that  is,  "  amberous,"  phenomena. 

243.  Electric  vs.  magnetic  attraction.     These  electric  at- 
tractions are  in  many  ways  so  much  like  magnetic  attractions 
that  it  was  not  until  the  sixteenth  century  that  it  was  clearly 
seen  that  two  very  different  kinds  of  phenomena  are  involved. 
Magnetization  can  be  produced  only  in  three  metals,  iron, 
nickel,  and  cobalt,  and  in  one  or  two  uncommon  alloys,  while 
electrification  can  be  produced  by  rubbing  almost  any  sub- 

248 


THE  BEGINNINGS   OF  ELECTRICITY  249 

stance,  especially  non-metals.  A  magnetized  body  always 
has  at  least  two  poles  where  its  magnetism  is  more  or  less 
concentrated,  and  these  poles  are  unlike,  for  if  one  of  them 
attracts  the  north-seeking  end  of  a  compass,  the  other  will 
always  repel  it.  A  metallic  body  electrified  by  friction  will 
ordinarily  not  have  its  properties  concentrated  in  spots,  and 
all  parts  of  it  will  act  very  much  alike  in  their  attracting 
power.  Nevertheless,  we  shall  presently  see  that  there  are 
two  kinds  of  electricity,  just  as  there  are  two  kinds  of 
magnetic  poles. 

244.  Conductors  and  insulators.  Some  substances  will  con- 
duct electricity,  while  others  will  not.  Thus  a  metal  sphere 
can  be  charged  with  electricity  by  touching  it  with  some 
electrified  substance,  such  as  a  stick  of  sealing  wax  which 
has  been  rubbed  with  a  cat's  skin,  if  the  sphere  is  suspended 
by  a  dry  silk  thread,  but  not  if  suspended  by  a  wire.  In  the 
latter  case  just  as  much  electricity  gets  into  the  sphere  as  in 
the  former,  but  it  all  runs  out  again  through  the  wire.  So 
we  distinguish  between  conductors,  the  best  of  which  are  the 
metals,  and  non-conductors  or  insulators,  such  as  dry  silk,  glass, 
hard  rubber,  sulphur,  porcelain,  paraffin,  and  resin.  It  is  to 
prevent  the  leakage  of  the  electricity  in  the  conductor  that 
electric  light,  telephone,  and  telegraph  wires  are  supported 
on  glass  or  porcelain  knobs  called  "  insulators." 

There  is  no  sharp  line  between  conductors  and  insulators  ; 
most  substances  conduct  a  little,  and  even  the  good  con- 
ductors vary  greatly  in  conductivity. 

In  the  following  table  a  few  common  substances  are  ar- 
ranged according  to  their  insulating  powers. 

INSULATORS  POOR  CONDUCTORS  GOOD  CONDUCTORS 

Amber  Dry  wood  Metals 

Sulphur  Paper  Gas  carbon 

Glass  Alcohol  Graphite 

Hard  rubber  Kerosene  Water  solutions  of 

Dry  air  Pure  water  salts  and  acids 


250  PRACTICAL  PHYSICS 

It  will  be  noticed  that  the  substances  which  can  be  easily 
electrified  by  friction  are  all  insulators.  One  reason  for 
this  is  that  when  electricity  is  generated  at  any  point  on 
a  body  by  rubbing,  it  stays  there  and  makes  its  presence 
known,  if  the  body  is  an  insulator ;  but  if  it  were  a  conduc- 
tor, the  electricity  would  leak  away  at  once. 

It  will  also  be  noticed  that  those  substances  which  are 
good  conductors  of  electricity  are  also  good  conductors  of 
heat.  This  curious  fact,  long  not  understood,  seems  to  be 
due  to  the  fact  that  both  heat  and  electricity  are  carried 
through  metals  by  a  swarm  of  tiny  particles,  called  elec- 
trons, which  drift  about  between  the  much  larger  molecules 
of  metal  like  wind  through  a  forest. 

245.  Positive  and  negative  electricity.     If  we  hang  up  in  a 
stirrup,  suspended  by  a  silk  thread,  a  glass  rod  which  has  been  rubbed 

with  silk,  and  then  bring  near  one  end  of  it 
another  glass  rod  which  has  also  been  rubbed, 
they  repel  each  other  (Fig.  208).  In  a  simi- 
lar way  two  hard  rubber  rods  or  sticks  of  seal- 
ing wax  repel  each  other.  But  when  we 
bring  a  rubbed  stick  of  sealing  wax  near  a 
rubbed  glass  rod  in  the  stirrup,  they  attract 
each  other. 

FIG.  208.  —  Two  electrified         From   such    experiments    as   these 

rods  repel  each  other.         1  -, .  , .    -11 

we  have  come  to  distinguish  be- 
tween two  states  of  electrification.  We  call  one  kind 
"  vitreous "  (glass)  electricity  or  positive  electricity,  and 
the  other  "  resinous "  electricity  or  negative  electricity. 
Bodies  charged  with  the  same  kind  of  electricity  repel  each 
other,  and  bodies  charged  with  different  kinds  of  electricity 
attract  each  other.  That  is, 

Like  charges  repel  and  unlike  charges  attract. 

246.  How  to  detect  electricity.     To  test  the  electrical  con- 
dition of  a  body  we  use  an  electroscope.     A  simple  form  of 


THE  BEGINNINGS   OF  ELECTRICITY 


251 


electroscope  consists  of  a  pith  ball  hung  by  a  silk  thread 
from  a  glass  support  (Fig.  209). 

If  an  uncharged  body  is  brought  near  the  pith 
ball,  nothing  happens.  If  a  positively  charged  body 
is  brought  near  the  pith  ball,  the  latter  is  attracted, 
becomes  itself  positively  charged,  and  is  then  repelled. 
Then  if  a  negatively  charged  body  is  brought  near, 
the  positively  charged  pith  ball  is  attracted,  but  when 
it  touches,  it  becomes  negatively  charged  and  flies 
back.  If  we  now  bring  a  negatively  charged  body 
near,  the  negatively  charged  pith  ball  is  repelled. 
If,  then,  we  know  what  the  nature  of  the  charge  on 
the  pith  ball  is,  and  find  that  a  body  repels  it,  we 
know  the  body  must  be  charged  the  same  way.  If 
there  is  attraction,  we  cannot  be  sure  whether  the 
body  is  uncharged  or  oppositely  charged. 


FJG.  209.- Pith-ball 
electroscope. 


A  more  reliable  form  of  electroscope  is  the  so-called  "  gold- 
leaf  "  electroscope,  although  nowadays  they  are  quite  commonly 
made  of  two  aluminum  leaves  hung 
from  a  brass  rod.  These  are  usually 
mounted  in  some  sort  of  a  glass  case, 
as  shown  in  figure  210. 

When  one  brings  near  the  top  of  the  brass 
rod  a  charged  glass  rod,  the  aluminum  leaves 
separate  and  hang  like  an  inverted  V.  If  the 
rod  is  removed,  the  leaves  come  together  again. 
If,  however,  one  actually  touches  the  charged 
rod  to  the  electroscope,  the  leaves  separate  and 
stay  apart. 

The  electroscope  is  then  said  to  be  charged. 
If  we  bring  near  a  positively  charged  electro- 
scope a  positively  charged  body,  the  leaves 
will  fly  farther  apart ;  but  if  the  body  brought 
near  has  a  negative  charge,  the  leaves  will 
fall  toward  each  other.  In  either  case  they  will  return  to  their  origi- 
nal charged  position  when  the  outside  charged  body  is  taken  away. 
So  with  an  electroscope  one  can  tell  the  electrical  condition  of  a 
body. 


FIG.  210.— The  aluminum- 
leal  electroscope. 


252 


PRACTICAL  PHYSICS 


With  such  an  electroscope  it  is  possible  to  learn  much 
about  electrified  bodies.  For  example,  when  an  insulated 
conductor  is  rubbed,  it  becomes  charged  with  electricity ; 
so  we  conclude  that  all  bodies  become  electrified  by  friction. 
If  we  stand  on  an  insulated  stool,  while  we  rub  a  glass  rod, 
our  body  becomes  negatively  charged ;  and  by  rubbing  seal- 
ing wax  with  cat's  fur,  we  become  positively  charged.  In 
general,  whenever  two  different  substances  are  rubbed  on  one 
another,  one  becomes  positively  charged  with  electricity,  while 
at  the  same  time  the  other  is  negatively  charged. 

247.  Frictional  electric  machine.  All  the  early  forms  of 
electrical  machines  were  frictional,  and  such  machines  are 
still  used  for  demonstration  purposes.  A  circular  glass 
plate  is  mounted  firmly  on  an  axle,  so  that  it  can  be  turned 
between  two  silk-covered  cushions,  which  are  pressed  against 
the  glass  by  springs.  The  charge  on  the  glass  is  drawn  off 
by  a  metal  comb  which  is  supported  on  a  glass  rod.  When 
the  plate  is  rotated,  it  becomes  positively  charged  and  this 

charges  the  metal  comb  positively; 
at  the  same  time  the  rubbers  be- 
come negatively  charged  and 
should  be  connected  with  the 
ground  by  a  wire  or  chain,  that 
is,  grounded,  so  that  the  negative 
charges  can  escape. 

248.  Distribution  of  electricity 
on  a  conductor.  Let  us  place  a  metal 
can,  such  as  is  used  for  heat  measure- 
ments, on  a  glass  plate  as  shown  in  fig- 
ure 211,  and  connect  it  with  an  electrical 
machine  by  a  wire.  After  we  have 
charged  the  can  as  much  as  possible,  we 
may  test  it  at  various  points  by  means 
of  a  little  metal  disk  or  ball  mounted 


FIG.  211.  -Charging  a  metal  can. 


on  an  insulating  handle  and  known  as  a  proof  plane.     If  we  touch  it  to 
the  outside  surface  of  the  charged  can  and  bring  it  near  the  knob  of 


THE  BEGINNINGS   OF  ELECTRICITY  253 

a  charged  electroscope,  and  then  repeat  the  test,  touching  it  to  the  inside 
surface,  we  find  that  there  is  a  strong  charge  on  the  outside  but  none  on 
the  inside. 

Such  experiments  show  that  the  charge  is  entirely  on  the 
outer  surface  of  a  conductor  and  that  its  greatest  density  is  at 
the  corners  and  projecting  points.  In  fact  the  density  of  the 
charge  at  sharp  points  is  so  great  that  the  charge  will  escape 
into  the  air  easily  at  such  points. 

If  we  attach  a  tassel  of  tissue  paper  to  the  insulated  conductor  of  the 
electric  machine  and  charge  it,  the  little  paper  streamers  repel  each  other 
and  stand  out  in  all  directions,  but  if  a  needle  point  is 
held  near  them,  they  fall  together  at  once. 

We  may  fasten  to  a  friction  machine  an  "  electric 
whirl,"  balanced  on  a  pin  point.  When  the  machine 
is  started,  the  whirl  turns  as  shown  in  figure  212. 

If  a  bent  point  is  attached  to  the  machine,  and  a 
candle  flame  is  held  near  the  point,  the  so-called  "  elec- 
tric wind  "  may  blow  the  candle  flame  aside.  It  is  not, 
however,  the  electricity  itself  that  blows  the  candle,  but 
the  surrounding  air  which  is  in  some  way  set  in  motion 
by  the  discharge. 

Such  experiments  show  that  a  conductor  can 
be  charged  or  discharged  more  easily  at  a  sharp        ^ric  whirlt 
point  than  at  a  rounded  surface. 

249.  Lightning  and  lightning  rods.  For  a  long  time  people 
supposed  that  thunder  and  lightning  were  caused  by  the  com- 
bustion of  some  kind  of  gas  in  the  clouds.  But  when  elec- 
tricity began  to  be  studied,  it  occurred  to  some  philosophers 
that  lightning  might  be  an  electrical  phenomenon.  Thus  we 
find  Benjamin  Franklin  in  his  notebook,  under  the  date  of 
November  7,  1749,  making  a  list  of  the  respects  in  which 
lightning  resembled  electric  sparks,  such  as  "giving  light, 
color  of  the  light,  crooked  direction,  swift  motion,  being  con- 
ducted by  metals,  crack  or  noise  in  exploding,  rending  bodies 
it  passes  through,  destroying  animals,  heating  metals  and 
kindling  inflammable  substances,  and  its  sulphurous  smell" 


254  PRACTICAL  PHYSICS 

(now  known  to  be  due  to  ozone).  He  then  wondered  ii 
lightning,  like  electricity,  could  be  drawn  off  by  points. 
"  Since  they  agree  in  all  the  particulars  wherein  we  can 
already  compare  them,  is  it  not  probable  that  they  agree  like- 
wise in  this?  Let  the  experiment  be  made." 

But  this  was  not  easy.  Franklin  thought  he  would  require 
a  tower  or  steeple  high,  enough  to  reach  into  the  clouds 
themselves,  and  his  friends  set  about  raising  the  money  to 
build  one  by  giving  popular  lectures  on  electricity  all  over 
the  country.  In  the  meantime  two  Frenchmen  were  bold 
enough  to  try  the  experiment  with  insulated  pointed  rods 
less  than  a  hundred  feet  high,  and  were  successful  in  drawing 
off  sparks  from  the  lower  ends  of  the  rods  during  thunder 
showers.  But  Franklin  was  not  satisfied,  because  the  rods 
did  not  reach  into  the  thunder  clouds,  and  might  have  been 
electrified  some  other  way.  Suddenly  in  1752  a  new  idea 
flashed  into  his  mind,  and  he  set  about  making  his  famous 
kite.  The  result  is  known  to  every  one.  Almost  the  most 
wonderful  part  of  it  was  that  Franklin  was  not  killed  at  once. 
Within  a  year  one  Richman  was  killed  while  making  a  similar 
experiment  in  St.  Petersburg. 

So  Franklin  invented  the  lightning  rod  to  conduct  elec- 
tricity safely  from  the  clouds  to  the  earth.  Nowadays  in 
cities  where  the  houses  are  built  in  blocks  with  frameworks, 
tops,  and  cornices  of  metal,  the  lightning  rod  is  not  much 
used.  But  tall  chimneys,  church  steeples,  and  isolated  houses 
are  often  provided  with  lightning  rods. 

It  should  be  remembered  that  unless  a  lightning  rod  is 
put  up  with  considerable  care,  it  is  a  menace  rather  than  a 
protection.  In  particular,  its  lower  end  must  be  well 
"  grounded,"  as  by  soldering  to  large  copper  plates  buried  in 
damp  soil,  and  no  part  of  the  rod  should  turn  a  sharp  corner. 
If  these  precautions  are  not  observed,  a  lightning  rod  will 
often  discharge  into  the  house  itself,  rather  than  into  the 
ground,  the  electricity  which  it  has  attracted. 


THE  BEGINNINGS  OF  ELECTRICITY  255 

QUESTIONS 

1.  Compare  the  behavior  of  a  magnetic  pole  with  the  behavior  of  an 
electrically  charged  body. 

2.  Does  a  freely  swinging  charged  body  take  a  definite  direction  ? 

3.  What  becomes  of  the  mechanical  energy  exerted  in  rubbing  a  glass 
rod  to  electrify  it  ? 

4.  What  kind  of  electricity  is  generated  by  rubbing  a  fountain  pen 
on  woolen  cloth  ? 

5.  Why  do  experiments  with  friction al  electricity  work  better  on  a 
cold,  dry  winter  day  V 

6.  Does  one  remove  magnetism  from  a  magnet  by  touching  it  with  iron? 

7.  Faraday  built  a  large  box  and  lined  it  with  tin  foil.     He  then  took 
his  most  sensitive  electroscope  into  the  box  and  found  that  even  when 
the  outside  of  the  tin  foil  was  so  charged  that  it  sent  forth  long  sparks, 
he  could  not  observe  any  electrical  effects  inside.     Explain. 

8.  What  evidence  have  you  that  the  human  body  is  a  good  conductor  ? 

250.  Charging  by  induction.  If  one  brings  a  positively 
electrified  ball  near  an  insulated  conductor,  such  as  a  metal 
cylinder  on  a  glass  support,  and  then  removes  it  again,  the 
cylinder  is  not  electrified.  But  if,  while  the  electrified 
body  is  near,  one  touches  the  cylinder  with  his  finger  or  a 
grounded  wire  for  an  instant,  the  cylinder  is  found  to  be 
negatively  charged  after  the  charged  body  has  been  removed. 
If  one  repeats  this  experiment  using  a  negatively  charged 
ball,  the  metal  cylinder  becomes  positively  charged.  Since 
the  electricity  is  not  diminished  in  the  ball,  we  must  look 
to  the  cylinder  for  the  electricity.  Charges  produced  in 
a  conductor  by  virtue  of  its  proximity  to  a  charged  body 
are  called  induced  charges. 

This  process  of  charging  by  induction  may   be  explained 
as  follows.      When  the  posi- 
tively charged  ball  is  brought 
near  the  cylinder,  the  positive 
and  negative  electricity  in  the       FlG-  213-  -  Charging  by  induction, 
cylinder  are  distributed  as  shown  in  figure  213. 

When  one  touches  the  cylinder,  the  positive  electricity, 


256 


PRACTICAL  PHYSICS 


which  is  repelled,  finds  its  way  to  the  ground  through  the 
body,  but  the  negative  electricity  remains  bound  (Fig.  214). 

It  does  not  flow  off 
when  the  conductor  is 
touched,  but  is  held 
by  the  presence  of  the 
charged  body. 

This    helps    us    to 


FIG.  214.  —  Bound  charge. 


O 


Fia.  215.  —  Charging  an  electro- 
scope by  induction. 


understand  the  gold-leaf  electroscope.       When    a   charged 

body   is   brought   near   the   knob  of   the  electroscope,  the 

leaves  separate  because  they  are 

charged   by   induction    with  the 

same  kind  of  electricity  as   the 

charged    body    (Fig.  215).       If 

the   electroscope   is   charged   by 

contact    positively   and    a    posi- 

tively charged  body  is  brought 

near,  it  repels  more  of  the  posi- 

tive  electricity   into   the   leaves 

and  so  they  diverge  more  widely. 

On  the  other  hand  if  a  negatively  charged  body  is  brought 

near,  it  draws  some  of  the  positive  electricity  up  into  the 

knob,  and  the  leaves  come  together  more  or  less  according 

to  the  amount  of  the  charge. 

251.    Condenser.     In   many  practical  applications  of  elec- 

tricity, it  is  necessary 
to  increase  the  capac- 
ity of  a  conductor  for 
holding  electricity. 

A  This  is  done   in   what 

/  \  is  called    a  condenser. 


t 


TO  earth 


FIG.  216.  —  Action  of  a  condenser. 


Let  us  arrange  a  metal 
plate  on  an  insulating  base 
and  connect  the  plate  by 
a  wire  to  an  electroscope,  as  shown  in  figure  216.  If  we  charge  the 
plate  A,  we  see  the  leaves  of  the  electroscope  diverge.  We  will  now 


THE  BEGINNINGS   OF  ELECTRICITY 


257 


bring  up  a  second  metal  plate  B  similar  to  plate  A,  but  connected  with 
the  ground.  As  we  bring  the  plate  B  near  plate  A,  the  electroscope 
leaves  begin  to  fall  together,  but  if  we  remove  plate  B  again,  the  leaves 
separate  as  before. 

Let  us  now  bring  the  plate  B  back  to  a  position  near  plate  A,  and 
charge  plate  A  until  it  shows  the  same  deflection  as  before.  It  will  be 
evident  that  the  capacity  of  plate  A  for  holding  electricity  is  much  in- 
creased by  being  close  to  a  similar  grounded  plate  B. 

We  may  also  show  the  influence  of  the  insulating  material  between 
the  conducting  plates,  by  introducing  a  pane  of  glass.  The  leaves  of 
the  electroscope  fall  nearer  together,  but  rise  again  when  the  glass  is 
removed.  This  shows  that  the  capacity  of  the  condenser  is  increased  by 
the  glass  plate. 

A  combination  of  conducting  plates  separated  by  an  insu- 
lajbor  is  called  a  condenser.  The  capacity  of  a  condenser  for 
holding  electricity  is  proportional  to  the  size  of  the  plates 
and  increases  as  the  distance  between  them  decreases.  It 
also  depends  on  the  nature  of  the  insulator,  or  dielectric,  as  it 
is  called.  Mica  and  paraffin  paper  are  much  used  in  com- 
mercial work. 

252.  Leyden  jar.  At  the  University  of  Leyden  in  Hol- 
land, as  early  as  1745,  they  used  a  condenser  in  the  form  of  a 
wide  jar  or  bottle  (Fig.  217),  coated  inside 
and  out  with  tin  foil.  Inside  the  jar,  and 
connected  at  the  bottom  to  the  inside  coating, 
is  a  rod  with  a  knob  on  top.  If  one  allows  a 
charge  of  positive  electricity  to  jump  to  the 
knob  the  positive  electricity  on  the  inner  lin- 
ing attracts  through  the  glass  the  negative  elec- 
tricity of  the  outer  coating,  while  at  the  same 
time  the  compensating  positive  electricity  origi- 
nally in  the  outer  coating  is  repelled  and  escapes 
through  its  support  or  the  hand  which  holds 
it.  It  is  possible  to  make  a  great  number 
of  sparks  jump  to  the  knob  before  it  ceases 
to  receive  them.  Then  the  jar  is  charged.  If  one  connects 
the  outer  coating  and  the  knob  by  a  metal  wire,  the  elec- 


FIG.  217. —Ley 
den  jar. 


258 


PRACTICAL  PHYSICS 


FIG.  218.  —  Hydraulic  analogy  of  a 
condenser. 


trical  strain  or  pressure  is  released  with  a  bright  crackling 
spark.  If  the  jar  is  discharged  through  a  piece  of  paper,  the 
spark  makes  a  hole  in  the  paper.  If  one  makes  the  connec- 
tion through  his  own  body,  he  feels  a  lively  sensation,  known 
as  a  shock. 

253.  Hydraulic  analogy  of  a  condenser.  We  may  illustrate 
a  condenser  by  two  standpipes  filled  to  different  levels  with 

water,  as  shown  in  figure  218. 
The  coatings  of  the  condenser 
correspond  to  the  standpipes. 
The  pipe  A,  with  the  water 
standing  at  a  higher  level,  rep- 
resents the  positively  charged 
plate  or  coating,  while  the 
other  pipe  B  is  the  negatively 
charged  plate.  The  connect- 
ing pipe  at  the  bottom  of  the 
tanks  corresponds  to  the  wire 
connecting  the  coatings.  When  the  connection  is  made, 
the  water  rushes  through  the  pipe  and  equalizes  its  levels 
very  quickly.  This  represents  the  discharge  of  the  con- 
denser. 

When  the  valve  V  in  the  pipe  is  first  opened,  the  water 
rushes  through  so  fast  that  it  usually  overdoes  things,  and 
rises  to  a  higher  level  in  B  than  in  A.  Then  it  flows  back 
again  and  so  on,  oscillating  back  and  forth  until  the 
motion  dies  out  because  of  friction  in  the  pipe.  In  much 
the  same  way,  when  a  condenser  is  short-circuited,  the  dis- 
charge of  electricity  goes  too  far  and  charges  up  the  condenser 
the  other  way.  Then  it  discharges  back  again,  arid  so  the 
electric  charges  oscillate  very  quickly  back  and  forth  until 
the  motion  of  the  electricity  dies  out  because  of  something 
akin  to  friction,  called  the  electrical  resistance  of  the  wire. 
The  technical  way  of  describing  this  is  to  say  that  the  dis- 
charge of  a  condenser  is  oscillatory. 


THE  BEGINNINGS   OF  ELECTRICITY 


259 


254.    Induction   machines   for   producing   electricity.     The 

simplest  machine .  for  producing  electricity  by  induction  is 
the     electrophorus.       It  ^ 

consists  of  a  hard 
rubber  disk  and  an- 
other somewhat  smaller  ,  fe:»  Nr-  A.(+  +  +  TD. 
metal  disk,  which  is 
provided  with  an  in- 
sulating handle  (Fig. 
219). 

If  we  rub  the  hard  rubber 
plate  of  an  electrophorus 
with  cat's  fur,  we  find  it 


(I 


/ Sit 

FIG.  219.  —  Electrophorus. 


is  charged  negatively.  Then  we  place  the  metal  disk  on  the  plate  and 
touch  the  finger  to  the  metal  disk  so  as  to  "  ground  "  it.  When  we  lift 
up  the  disk  and  bring  it  near  the  knuckle,  or  the  knob  of  a  Leyden  jar, 
a  spark  jumps  across  the  gap.  We  may  charge  a  Leyden  jar  with  an 
electrophorus  by  repeating  this  process  again  and  again. 

When  the  rubber  plate  is  electrified,  it  becomes  negatively 
charged.  When  the  metal  disk  is  placed  upon  it,  a  positive 
charge  is  attracted  to  the  lower  surface  of  the  disk  next  to 
the  plate,  while  the  negative  electricity  is  repelled.  When 
we  touch  the  metal  disk,  this  negative  electricity  escapes 
through  the  hand  to  the  ground.  In  this  process  the  disk 
becomes  charged  positively  throughout.  After  the  rubber 

plate  is  once  charged,  any 
number  of  charges  can  be 
obtained  from  the  electro- 
phorus, without  producing 
any  appreciable  change  in 
the  charge  on  the  plate. 
This  is  because  the  energy 
comes  from  the  agent  who 
lifts  the  disk. 

255.     Toepler-Holtz    ma- 

FIG.  220.  —  Toepler-Holtz  machine.  Chine.       Among    the    ma- 


260  PRACTICAL  PHYSICS 

chines  which  make  use  of  this  principle  of  induction  to  pro- 
duce electricity  is  the  so-called  Toepler-Holfcz  machine,  shown 
in  figure  220.  The  details  of  construction  are  so  many,  and 
the  explanation  of  its  operation  is  so  complex,  that  it  is  left 
to  the  special  books  on  electricity.  If  one  of  these  machines 
is  in  working  order,  many  entertaining  experiments  can  be 
done  with  it. 

256.  Theories  as  to  the  nature  of  electricity.  To  explain 
these  electrical  phenomena,  du  Fay,  a  Frenchman,  assumed 
that  there  were  in  all  bodies  two  fluids,  namely  vitreous 
electricity  and  resinous  electricity.  When  these  are  present 
in  equal  quantities,  they  neutralize  each  other.  If  a  glass 
rod  is  rubbed  by  silk,  the  silk,  which  has  a  greater  "  affinity  " 
for  the  resinous  fluid  than  the  glass,  absorbs  some  of  it  from 
the  glass,  and  at  the  same  time  the  glass,  having  a  greater 
affinity  for  the  vitreous  fluid  than  the  silk,  absorbs  some 
from  the  silk.  So  each  body  gets  an  excess  of  its  preferred 
fluid  and  becomes  charged. 

Later  Franklin  suggested  that  there  was  only  one  kind 
of  fluid,  namely,  vitreous  electricity,  of  which  a  certain 
amount  "  belonged  "  in  every  body.  If  it  had  an  excess, 
it  was  what  had  been  called  vitreously  charged.  If  it  had 
less  than  enough,  it  was  resinously  charged.  This  led  to 
the  terms  "  positive "  and  "  negative  "  charge,  which  are 
still  in  use. 

Lately,  we  have  come  back  to  something  nearer  du  Fay's 
idea.  We  do  not  think  of  electricity  as  a  kind  of  matter,  as 
the  word  "fluid"  indicates,  but  we  believe  that  there  are 
two  kinds,  a  negative  or  resinous  kind  occurring  in  very 
small  lumps  which  we  now  call  corpuscles  or  electrons,  and 
a  positive  kind  of  a  different  nature,  not  yet  understood. 
Even  in  the  modern  electron  theory,  however,  there  are  some 
who  prefer  to  believe  with  Franklin  that  there  is  only  one 
kind  of  electricity,  namely  electrons,  which  may  be  present 
either  in  excess  or  in  defect.  If  this  turns  out  to  be  true, 


THE  BEGINNINGS   OF  ELECTRICITY  261 

Franklin's  only  mistake  was  that  he  hit  on  the  wrong  kind 
of  electricity  as  positive. 

It  makes  very  little  difference  whether  we  talk  and  think 
in  terms  of  the  one-fluid  or  the  two-fluid  theory,  inasmuch 
as  everything  we  know  can  be  expressed  either  way,  and  we 
do  not  yet  know  which  is  right. 

257.  Conclusion.  Practically  all  that  people  knew  about 
electricity  up  to  the  beginning  of  the  nineteenth  century  has 
been  briefly  outlined  in  this  chapter  in  very  much  the  order 
in  which  it  was  discovered.  Few  discoveries  were  made,  and 
they  dealt  only  with  electricity  at  rest  (electrostatics).  Almost 
the  only  useful  electrical  invention  was  the  lightning  rod, 
and  its  usefulness  has  been  much  overestimated.  The  most 
useful  instrument  which  had  been  devised  was  the  condenser. 
Nevertheless,  the  people  of  the  eighteenth  century  were  fas- 
cinated by  electricity.  It  was  the  most  exciting  topic  with 
which  scientific  men  dealt;  it  was  lectured  about  and 
shown  off  to  large  audiences,  and  was  as  much  talked 
about  by  everybody  as  radium  or  wireless  telegraphy  have 
been  recently.  But  it  was  merely  a  plaything  in  labora- 
tories. 

In  the  last  half  of  the  nineteenth  century,  as  we  shall  see 
in  the  following  chapters,  electricity  suddenly  leaped  into  a 
commanding  position  in  the  arts  and  engineering.  Probably 
no  more  spectacular  service  has  ever  been  rendered  to  the 
welfare  of  mankind  by  what  practical  men  like  to  call  "  pure 
science."  The  story  of  this  development  is  a  most  convinc- 
ing answer  to  those  who,  even  now,  distrust  "pure  science" 
as  "  impractical  "  and  "  useless." 


SUMMARY   OF   PRINCIPLES    IN    CHAPTER   XIV 

All   bodies  can  be  electrified   by  friction,   becoming   charged 
either  positively  (vitreously)  or  negatively  (resinously). 


262  PRACTICAL   PHYSICS 

Like  charges  repel  each  other. 

Unlike  charges  attract  each  other. 

All  conductors  can  be  electrified  by  induction,  showing  both 
a  positive  and  a  negative  charge  in  different  places.  Of  these  one 
is  bound  by  the  inducing  charge,  but  the  other  is  free. 

QUESTIONS 

1.  Why  cannot  a  Leyden  jar  be  appreciably  charged  if  the  jar  stands 
on  a  glass  plate  ? 

2.  If  a  charged  Leyden  jar  is  placed  on  a  glass  plate,  why  does  one  not 
get  a  shock  if  he  touches  the  knob  ? 

3.  How  would  you  arrange  four  Leyden  jars  to  get  increased  capacity  ? 

4.  How  would  you  arrange  four  Leyden  jars  to  get  as  long  a  spark  as 
possible  ? 

5.  If  an  insulated  metal  globe  is  negatively  charged,  how  can  any 
number  of  other  insulated  globes  be  positively  charged  ? 

6.  If  an  insulated  metal  globe  is  negatively  charged,  how  can  any 
number  of  other  insulated  rnetal  globes  be  negatively  charged? 

7.  In  the  experiment  shown  in  figure  214,  why  must  the  finger  be 
removed  before  the  removal  of  the  charged  body? 


CHAPTER   XV 


BATTERY   CURRENTS 

The  voltaic  cell  —  action  in  a  cell  —  hydraulic  analogy  —  de- 
fects of  simple  cell  —  commercial  cells. 

Magnetic  field  around  a  current,  and  around  a  coil  —  electro- 
magnet —  electric  bell  —  telegraph. 

BATTERIES 

258.  Beginnings  of  the  electric  battery.     For  nearly  two 
thousand  years  friction  and  induction  were  the  only  meth- 
ods  known   for   producing   electricity.      But,    in    1786,    an 
unexpected  observation  of  an  Italian  anatomist,  Galvani,  in 
Bologna,  started  a  series  of  most  important  discoveries  and 
inventions.     He  observed  that  the  legs  of  frogs  which  he  had 
been  dissecting  twitched  every  time  there  was  a  discharge 
from  his  electric  machine.     Later  he  found  that  if  strips  of 
two  different  metals,  such  as  copper  and  zinc,  were  fastened 
together  like  an  inverted  V,  and  their  free  ends  applied  to  frogs' 
legs,  there  were  the  same  nervous  twitchings  as 

followed  the  discharge  of  electricity.  There- 
fore he  concluded  that  he  had  found  a  new  way 
of  producing  electricity.  He  thought  the  elec- 
tricity was  formed  at  the  contact  of  the  dissimi- 
lar metals. 

While  -investigating  this  question,  Volta 
invented  a  chemical  method  of  producing  elec- 
tricity continuously,  called  an  electric  battery. 

259,  Voltaic  battery.     A  glass  tumbler,  with 

a  strip  of  zinc  and  a  strip  of  copper  dipping  into  dilute  sul- 
phuric acid  (Fig.  221),  is  one  form  of  voltaic  cell,  and  when 
several  cells  are  combined,  they  constitute  a  battery. 

263 


Dilute  Sul- 
phuric Acid 

FIG.  221.  —  Vol- 
taic cell. 


264 


PRACTICAL  PHYSICS 


FIG.  222.  —  To  show 
charges  on  plates 
of  voltaic  cell. 


To  show  that  the  copper  and  zinc  strips  are  each  charged  with  electric- 
ity, we  will  connect  six  such  cells  in  series  as  shown  in  figure  222.  To 
detect  the  feeble  charge  we  will  put  a  3-inch  disk 
on  the  top  of  the  brass  rod  of  the  aluminum- 
leaf  electroscope.  Then  we  will  take  another 
similar  disk  which  is  provided  with  an  insulating 
handle  and  has  a  thin  coating  of  shellac  on  the 
bottom,  and  place  this  disk  on  top  of  the  other. 
This  forms  a  condensing  electroscope.  If  we  touch 
the  wires  leading  from  the  zinc  and  copper  strips  of 
the  battery  to  the  lower  and  upper  disks  of  the  con- 
Zn  denser,  as  shown  in  figure  222,  and  then  remove  the 
wires  and  lift  off  the  upper  disk,  we  find  that  the 
leaves  of  the  electroscope  diverge.  If  we  bring  a 
charged  stick  of  sealing  wax  near  the  electroscope, 
the  leaves  spread  still  farther  apart,  which  shows 
that  the  electroscope  and  the  zinc  are  negatively  charged. 

If  we  repeat  the  experiment  with  the  wires  reversed,  we  can  show  that 
the  copper  is  positively  charged. 

The  copper  (or  the  carbon  which  often  replaces  it)  is  called 
the  positive  electrode  ojM-  pole,  while  the  zinc  is  called  the 
negative  electrode  or_—  jx>le.  The  solution  in  the  cell  is 
called  the  electrolyte.  When  the  poles  of  a  cell  are  joined 
by  a  conductor,  we  have  an  electric  path  or  circuit  con- 
sisting of  the  electrodes,  the  electrolyte,  and  the  metallic 
conductor  joining  the  poles.  If  a  bell  or  lamp  is  to  be  oper- 
ated by  an  electric  battery,  it  is  so  connected  that  the  elec- 
tricity passes  through  it  as  a  part  of  the  circuit.  When 
this  circuit  is  broken  at  any  point  by  a  switch,  key,  or  push 
button,  so  that  no  electricity  jumps  the  gap,  the  circuit  is 
said  to  be  open.  When  the  switch  or  key  is  closed  so  as  to 
make  a  continuous  path,  the  circuit  is  said  to  be  closed  or  made. 

260.  Action  of  an  electric  cell.  We  have  already  seen  that 
when  a  Leyden  jar  is  discharged,  or  any  two  charged  bodies  are 
connected  by  a  wire,  there  is  what  we  call  a  flow  of  electricity ; 
that  is,  an  electric  current.  By  convention  we  say  that  the 
electricity  in  the  connecting  wire  flows  from  the  positive  to  the 
negative  conductor.  In  a  single  electric  cell  we  shall  speak, 


BATTERY  CURRENTS  265 

therefore,  of  the  electricity  as  flowing  through  the  outside 
circuit  from  the  copper  or  carbon  electrode  (-hpole)  to  the 
zinc  electrode  (—  pole).  Inside  the  cell  the  electricity  must 
evidently  flow  "  uphill "  through  the  solution  or  electrolyte 
back  to  the  copper  electrode.  We  shall  see  presently  why 
it  is  able  to  flow  uphill  inside  the  cell. 

To  understand  a  little  better  just  what  is  happening  inside  the  cell, 
let  us  dip  a  strip  of  ordinary  zinc  into  very  dilute  sulphuric  acid.  We 
shall  see  bubbles  rising  from  the  zinc  and  coming  to  the  surface  of  the 
acid.  These  bubbles  are  a  gas  called  hydrogen.  If  we  leave  the  zinc  in  the 
acid,  it  gradually  dissolves,  leaving  behirioTonly  a  few  insoluble  impurities. 

If  we  repeat  the  experiment,  using  a  copper  strip,  we  shall  find  no 
action ;  but  if  we  put  both  the  zinc  and  the  copper  strips  into  the  acid 
and  connect  them  with  copper  wires  to  some  instrument  that  indicates  a 
current  of  electricity  (a  galvanometer),  we  see  that  a  current  is  produced, 
and  that  bubbles  are  coming  from  both  the  copper  and  the  zinc  strips. 

Next  we  will  remove  the  zinc  strip  and  rub  a  little  mercury  on  it. 
The  mercury  clings  to  the  zinc  and  can  be  spread  over  its  surface.  Such  a 
union  of  a  metal  with  mercury  is  called  amalgamation.  If  this  amalga- 
mated zinc  is  used  in  the  cell,  no  bubbles  are  formed  on  it.  When  the 
circuit  is  closed,  bubbles  rise  from  the  copper  plate,  and  when  the  circuit 
is  broken  or  open,  these  bubbles  stop.  A  galvanometer  in  the  circuit 
shows  a  current  as  before,  but  now  the  amalgamated  zinc  is  consumed 
only  when  the  circuit  is  closed.  The  copper  is  not  consumed  by  the  acid 
at  all. 

In  general  it  can  be  said  that  the  electric  current  depends 
on  the  difference  in  the  chemical  action  of  the  acid  on  the 
two  metals  used  as  electrodes.  The  metal  which  is  dissolved 
or  acted  upon  by  the  acid  is  the  negative  electrode ;  the 
metal  which  is  apparently  unchanged  and  from  which  the 
hydrogen  bubbles  rise  while  the  circuit  is  closed  is  the  posi- 
tive electrode. 

261.  The  chemistry  of  the  cell.  In  chemistry  we  learn 
that  sulphuric  acid  is  made  up  of  two  parts  hydrogen,  one 
part  sulphur,  and  four  parts  oxygen,  as  expressed  by  the 
symbol  H2SO4.  When  sulphuric  acid  is  dissolved  in  water, 

some  of  it  breaks  up  into  two  parts,  H2  and  SO4.     These 


266 


PRACTICAL  PHYSICS 


two  parts,  called   ions,  carry  opposite   kinds   of   electricity. 

+  + 
The  H2   is   positively  charged  and    the  SO4   is    negatively 

charged. 

When  zinc  (Zn)  is  placed  in  the  acid,  a  little  of  it  dis- 

+  + 
solves,  becoming  zinc  ions  (Zn),  which  unite  with  the  SO4 

ions  to  form  zinc  sulphate  (ZnSO4).      The  displaced  hydro- 

+  + 
gen  (H2)  goes  to  the  copper  plate,  gives  up  its  charge  to  the 

plate,  and  then  rises  as  bubbles  of  gas.  It  is  important  to 
remember  that  the  positively  charged  part  of  the  electrolyte 

(H2)  goes  with  the  current  through  the  cell.  The  electric 
current  will  flow  through  the  wire  from  the  copper  to  the 
zinc  as  long  as  the  chemical  action  is  maintained.  Thus  we 
see  that  it  is  the  energy  of  the  chemical  action  which  forces 
the  electricity  to  run  uphill  inside  the  cell.  In  this  way 
chemical  energy  is  transformed  into  electrical  energy. 

In  a  good  commercial  cell  the  chemical  action  takes  place 
only  when  the  cell  is  delivering  electrical  energy.  The  rate 
at  which  this  energy  is  delivered  by  the  cell  determines  the 
rate  at  which  the  zinc  is  used  up ;  just  as  the  rate  at  which 
steam  energy  is  delivered  by  a  boiler  determines  the  rate  of 
coal  consumption.  Zinc  is,  then,  the 
fuel  of  the  electric  cell. 

262.  Electric  currents  and  water 
currents.  Although  it  must  not  be 
supposed  that  electricity  is  a  material 
flowing  through  the  circuit  as  water 
flows  through  a  pipe,  yet  it  will 
greatly  help  us  to  form  a  mental  pic- 
ture of  the  situation  if  we  compare 
electric  currents  with  water  currents. 
FIG.  223,-Water  at  different  In  figure  223  we  have  two  tall  open 

vessels  containing  water.     These  are 

connected  by  a  pipe  which  contains  a  pump  driven  by  the 
weight  W.  The  water  will  evidently  be  pumped  from  A  to  J9? 


w 


BATTERY  CURRENTS 


267 


FIG.  224. —Water  iu  circu- 
lation. 


until  the  back  pressure  on  the  pump  due  to  the  higher  level 
of  the  water  in  B  is  enough  to  balance  the  weight  W.  This 
difference  in  level  does  not  depend  on 
the  size  of  the  vessels. 

Suppose  now  that  the  vessels  are 
connected  by  a  second  pipe,  as  shown 
in  figure  224.  Then  the  difference 
in  levels  will  cause  the  water  to  flow 
from  B  to  A.  The  water  level  in  B 
drops  a  little  and  that  in  A  rises,  so 
that  the  difference  in  levels  between 
A  and  B  becomes  less.  When  the 
back  pressure  against  the  wheel  of 
the  pump  is  thus  reduced,  the  weight 
drops  and  drives  the  water  around  the  circuit.  This  will 
continue  as  long  as  the  weight  can  move  downward. 

The  difference  in  level  in  A  and  B,  in  figure  223,  repre- 
sents the  difference  in  the  electrical  condition  of  the  two 
electrodes,  copper  and  zinc.  This  is  called  the  difference  of 
potential  between  the  positive  and  negative  poles  of  the  cell. 
The  pump  represents  the  chemical  action  of  the  acid  on  the 
zinc,  which  produces  this  difference  of  potential.  Figure  223 
is,  then,  analogous  to  the  cell  with  its  circuit  open. 

The  cell  with  its  circuit  closed  is  represented  by  figure  224. 
The  tube  connecting  A  and  B  represents  the  outside  circuit 
between  the  copper  and  the  zinc.  The  circulation  of  the 
water  represents  the  flow  of  electricity.  The  rate  at  which 
the  water  circulates  depends  on  the  difference  in  level  which 
the  pump  can  maintain  ;  that  is,  on  the  power  of  the  pump. 
Similarly  the  rate  of  flow  of  electricity  depends  on  the 
electromotive  force  which  the  chemical  action  of  the  acid  and 
zinc  can  maintain.  Furthermore,  the  rate  of  flow  of  the 
water  depends  on  the  friction  in  the  connecting  pipes,  and 
similarly,  the  rate  of  flow  of  the  electricity  depends  on  the 
electrical  friction  or  resistance  of  the  circuit.  Finally,  just 


268 


PRACTICAL   PHYSICS 


as  the  energy  needed  to  circulate  the  water  comes  from  the 
action  of  gravity  on  the  weight,  so  the  energy  needed  to  drive 
the  electric  current  is  supplied  by  the  chemical  changes  which 
take  place  at  the  electrodes. 

263.  Two  defects  in  a  simple  cell.  Volta's  simple  cell, 
which  has  been  described,  was  soon  found  to  have  two 
defects,  local  action  and  polarization.  When  ordinary  zinc 
is  used,  bubbles  of  hydrogen  are  formed  at  the  surface  of  the 
zinc  strip  even  before  it  is  connected  with 
the  copper.  This  means  a  wearing  away 
of  the  zinc  to  no  purpose,  and  is  called 
local  action.  It  is  due  to  impurities,  such 
as  iron  or  carbon,  embedded  in  the  zinc. 
These  impurities  form  with  the  zinc  a 
minute  voltaic  cell,  as  shown  in  figure  225. 
The  local  current  flows  from  the  iron  or 
carbon  directly  to  the  zinc  and  then  back 
through  the  acid  to  the  iron  again.  In 
this  process,  the  zinc  is  eaten  away  near 
FIG.  225.  —  Local  ac-  the  impurity,  and  hydrogen  is  set  free.  To 
tion  in  a  cell.  avoid  this  useless  wasting  away  of  the  zinc, 
it  is  necessary  to  use  strictly  pure  zinc  or  else  to  amalgamate 
the  zinc  electrode  with  mercury  to  cover  up  the  impurities. 

The  second  defect  is  the  fact  that,  when  the  poles  of  a 
simple  cell  are  connected  by  a  wire,  the  current  does  not 
remain  constant,  but  rapidly  gets  weaker.  This  polarization, 
as  it  is  called,  is  caused  by  the  hydrogen  bubbles  which  col- 
lect on  the  copper  strip  and  thus  form  a  gaseous  coating. 
This  layer  of  hydrogen  is  a  poor  conductor  of  electricity  and 
therefore  weakens  the  current.  Furthermore  the  hydrogen 
layer  has  a  slight  battery  action  of  its  own,  tending  to  send 
a  current  in  a  direction  opposite  to  that  desired,  and  this 
also  weakens  the  current  delivered  by  the  cell. 

Let  us  set  up  a  zinc-sulphuric-acid-copper  cell,  connect  it  to  a  high 
resistance  galvanometer,  and  observe  the  deflection.  If  we  then  short- 


?U|— 

Zi 

~ 

Carbon 
80$ 

j 

1 

1 

BATTERY  CURRENTS 


269 


circuit  the  poles  of  the  cell  by  a  short  wire,  which  polarizes  the  cell 
quickly,  we  shall  observe,  on  removing  the  wire,  that  the  deflection  is 
less  than  before.  We  may  restore  the  cell  by  lifting  the  copper  plate 
out  of  the  acid  for  a  moment  or  by  brushing  off  the  hydrogen  bubbles. 

We  may  also  show  polarization  in  a  carbon-zinc  cell  in  a  similar  way, 
but  we  can  easily  restore  the  cell  by  pouring  into  the  acid  a  solution  of 
potassium  dichromate,  a  substance  rich  in  oxygen.  This  increases  the 
current  because  the  hydrogen  is  taken  up  chemically  by  the  oxydizing 
agent.  If  we  now  "  short-circuit  "  the  cell,  that  is,  connect  the  terminals 
with  a  low-resistance  conductor,  the  cell  recovers  quickly  when  the  short 
circuit  is  removed.  Such  a  substance  as  the  potassium  dichromate  is 
called  a  depolarizer. 

264.  Commercial  cells.  There  is  a  two-fluid  cell,  called 
the  Daniell  cell,  which  is  free  from  polarization.  In  this  cell 
the  copper  plate  (Cu)  stands  in  a  solution  of  copper  sulphate 
or  blue  vitriol  (CuSO4)  and  the  zinc  (Zn)  in  a  solution  of 
zinc  sulphate  (ZnSO4).  Both  the  copper  sulphate  and  the 
zinc  sulphate  break  up  into  ions.  When  the  circuit  is 
closed,  both  copper  and  zinc  ions  carry  the  current  toward 
the  copper  electrode.  The  zinc  ions,  however,  do  not  reach 
the  copper  plate,  because  zinc  in  copper  sulphate  replaces 
copper,  forming  zinc  sulphate.  The  result 
is  that  the  zinc  goes  into  a  solution  form- 
ing zinc  sulphate,  and  metallic  copper  is 
deposited  on  the  copper  electrode. 

One  form  of  this  cell,  much  used  in  teleg- 
raphy, is  called  a  gravity  cell  (Fig.  226) 
because  the  two  liquids  are  separated  by 
gravity.  The  dilute  solution  of  zinc  sul- 
phate is  lighter  and  therefore  floats  on 
the  saturated  solution  of  copper  sulphate. 
The  copper  plate  in  the  bottom  of  the  jar 
is  surrounded  by  crystals  of  copper  sul-  FIG.  226.  — Gravity 
phate  to  keep  the  solution  saturated.  In 
the  dilute  zinc-sulphate  solution  above  is  a  heavy  piece  of 
zinc  in  the  shape  of  a  "  crowfoot." 


270 


PRACTICAL   PHYSICS 


If  the  gravity  cell  is  allowed  to  stand  with  its  circuit  open, 
the  liquids  mix  slowly,  and  copper  is  deposited  on  the  zinc  in 
long  festoons  which  cause  local  action,  and  sometimes  grow 
long  enough  to  short-circuit  the  cell.  To  prevent  this,  the 
external  circuit  must  be  kept  closed.  The  cell  is  therefore 
well  adapted  for  telegraphy,  where  a  small,  constant  current 
is  needed,  but  is  not  good  for  ringing  doorbells  or  other 
intermittent  work.  In  another  form  of  Daniell  cell,  the 

solutions  are  sep- 
arated by  a  cup 
of  porous  earthen- 
ware. 

For  open-circuit 
work,  such  as  ring- 
ing doorbells,  the 
sal-ammoniac  cell 
(Fig.  227)  is  used. 
The  electrodes  are 
zinc  and  carbon, 
and  the  electrolyte 
is  a  solution  of  sal- 
ammoniac  (ammonium  chloride,  NH4C1).  To  reduce  the 
polarization  as  much  as  possible,  the  carbon  electrode  is  made 
with  a  large  surface,  and  the  cell  often  contains,  as  a  depolar- 
izer, a  mixture  of  carbon  and  manganese  dioxide.  Since  this 
depolarizer  is  slow  in  its  action,  the  cell  is  adapted  only  to 
open-circuit  work.  It  gives  off  no  fumes,  has  very  little 
local  action,  and  so,  when  once  set  up,  requires  very  little 
attention.  Occasionally  the  water  which  has  evaporated 
must  be  replaced  and  the  zinc  renewed. 

The  type  of  cell  now  most  used  for  small  intermittent 
work  is  the  dry  cell.  This  differs  from  the  sal-ammoniac 
cell  just  described  only  in  that  the  electrolyte  is  in  the  form 
of  a  paste  instead  of  being  a  liquid.  The  negative  electrode 
is  the  zinc  can  which  contains  the  carbon  and  paste 


FIG.  227.  —  Sal-ammoniac  cell. 


BATTERY  CURRENTS 


271 


(Fig.  228).  The  zinc  is  protected  on  the  inside  by  several 
layers  of  blotting  paper,  and  the  space  around  the  carbon  is 
filled  with  a  mixture  of  carbon,  man- 
ganese dioxide,  and  sawdust,  saturated 
with  a  solution  of  sal-ammoniac.  The 
top  is  sealed  with  wax,  and  the  whole 
cell  is  slipped  into  a  pasteboard  box. 

The  dry  cell  is  much  used  for  ringing 
doorbells,  running  clocks,  and  operating 
the  spark  coils  used  to  ignite  gas  engines 
on  boats  and  automobiles.  It  requires 
no  attendance,  but  must  not  be  left  on 
closed  circuit.  Sometimes  the  life  of 


U 


FIG.  .228.  —  Dry  cell. 


an  exhausted  dry  cell  can  be  extended  slightly  by  punching 
a  hole  in  the  top  and  pouring  in  water,  but  usually  exhausted 
cells  are  thrown  away. 


QUESTIONS 

1.  What  are  the  points  which  a  good  cell  should  possess? 

2.  Why  would  you  not  use  a  gravity  cell  for  ringing  a  doorbell  ? 

3.  What  is  the  "  fuel  "  in  the  dry  cell  ? 

4.  Why  are  the  small  motors  for  fans,  sewing  machines,  etc.,  never 
run  by  batteries  if  any  other  source  of  power  is  available  ? 

5.  If  a  person  touches  the  poles  of  a  cell,  why  does  he  not  get  a 
"  shock  "  ? 

6.  If  you  touch  the  two  wires  from  a  dry  cell  to  the  tip  of  your  tongue, 
do  you  taste  anything,  and  if  so,  why? 

MAGNETIC  EFFECT  OF  ELECTRIC  CURRENT 

265.  Oersted's  discovery.  In  1819  a  Danish  physicist, 
Oersted,  made  a  discovery  which  aroused  the  greatest  inter- 
est because  it  was  the  first  evidence  of  a  connection  between 
magnetism  and  electricity.  He  found  that  if  a  wire  connect- 
ing the  poles  of  a  voltaic  cell  was  held  over  a  compass  needle, 
the  north  pole  of  the  needle  was  deflected  toward  the  west 


272 


PRACTICAL  PHYSICS 


Wire  above    Wire  under   Prmfjnprnr 
needle  needle  [CtOr' 


when  the  current  flowed  from  south  to  north,  as  shown  in 
figure  229,  while  a  wire  placed  under  the  compass  needle 
caused  the  north  end  of  the  needle  to  be 
deflected  toward  the  east. 

266.    Magnetic  field  around  a  current. 
Inasmuch  as   the  compass    needle   indi- 
cates the  direction  of  magnetic  lines  of 
force,  it  is  evident   from    Oersted's  ex- 
periment that  a  current  must  set  up  a 
magnetic   field    at    right    angles   to   the 
To    make    this    clear,    the 
FIG.  229.  —  Deflection  of    student  may  perform  the  following  ex- 
magnetic  needle  by    periment. 
electric  current. 

We  will  send  a  strong  current  down  a  vertical 

wire  which  passes  through  a  horizontal  piece  of  cardboard.  To  indicate 
the  magnetic  lines  of  force,  we  will  sprinkle  iron  filings  on  the  cardboard 
and  tap  it  gently 

while  the  current  is  Jfy  f  ^\ 

on.  The  filings  ar-  "^ 
range  themselves  in 
concentric  rings 
about  the  wire.  By 
placing  a  small  com- 
pass at  various  posi- 
tions on  the  board, 
we  see  that  the  di- 
rection of  these  lines 
of  force  is  as  shown 
in  figure  230. 

A  convenient  rule  for  remembering  the  direction  of  the 
magnetic  flux  around  a  straight  wire  carrying  a  current  is  the 

so-called  thumb  rule. 

If  one  grasps  the  wire  with  the 
right  hand  (Fig.  231)  so  that  the 
FIG.  231.  — Thumb  rule  for  mag-    thumb    points    in   the   direction    of 

netic  field  around  a  wire.  ,7  .7        /;  -77         „'* 

the    current,   the  fingers  will  point 
in  the  direction  of  the  magnetic  field. 


Fia  230.  —  Magnetic  lines  of  force  around  a  current. 


BATTERY  CURRENTS 


273 


If  we  know  the  direction  of  the  magnetic  field  near  a  con- 
ductor, we  can,  by  applying  this  rule,  find  the  direction  of  the 
current. 

Figure  232  shows  the  field  around  the  wire  with  the  current 
going  in  and  figure  233,  with  the  current  coming  out. 


FIG.  232.  — Current  going  in,  clock- 
wise field. 


Fio.  233.  —  Current  coming  out,  anti- 
clockwise field. 


267.  Magnetic  field  around  a  coil.  If  a  wire  carrying  a  cur- 
rent is  bent  into  a  loop,  all  the  lines  of  force  enter  the  loop 
at  one  face  and  come  out  at  the  other  face.  If  several  loops 
are  put  together  to  form  a  coil,  practically  all  the  lines  will 
thread  the  whole  coil  and  return  to  the  other  end  outside  the 
coil. 

(1)  We  may  thread  a  loose  coil 
of  copper  wire  through  a  board 
or  sheet  of  celluloid  in  such  a 
way  that  when  iron  filings  are 
evenly  scattered  over  the  smooth 
surface  of  the  board,  while  a 
strong  current  is  sent  through 
the  wire,  they  will  indicate  the 
lines  of  magnetic  force  (Fig. 
L'34).  By  tapping  the  board 
gently  and  using  a  small  com- 
pass, we  can  see  the  general  di- 
rection of  th<*  lines  of  magnetic 
flux.  It  will  be  noticed  that 

there  are  a  few  circular  lines  around  each  wire,  arid  that  these  lines  go 
out  between  the  loops.     They  are  called  the  "  leakage  flux  "  of  the  coil. 


FIG.  234.  —  Magnetic  flux  around  a  coil. 


274  PRACTICAL   PHYSICS 

(2)  tf  we  send  a  current  through  a  close-wound  coil  of  insulated  copper 
wire,  and  bring  it  near  a  compass  needle,  we  find  that  it  behaves  like  a 
bar  magnet.    If  the  current  is  reversed,  the  poles  of  the  coil  are  reversed. 

(3)  If  we  put  a  soft  iron  core  inside  the  coil  when  the  current  is  on, 
the  iron  exerts  a  very  strong  pull  on  bits  of  iron  ;  but  when  the  current 
is  off,  the  iron  loses  this  magnetism  almost  at  once. 

(4)  If  we  use  a  large  horseshoe  electromagnet,  or  a  model  of  a  mag- 
netic hoist,  and  considerable  current,  we  may  show  that  a  tremendous 
force  can  be  exerted  by  an  electromagnet. 

An  iron  core  in  a  coil  of  wire  is  so  much  more  permeable 
than  air  that  the  same  current  in  the  same  coil  produces 
several  thousand  times  as  many  lines  of  forces  in  the  iron 
core  as  it  would  in  air  alone. 

268.  Electromagnet.  An  iron  core,  surrounded  by  a  coil 
of  wire,  is  called  an  electromagnet.  It  owes  its  great  utility 
not  so^  much  to  the  fact  of  its  great  strength,  as  to  the  fact 
that,  if  it  is  made  of  soft  iron,  its  magnetism  can  be  controlled 
at  will.  Such  an  electromagnet  is  a  magnet  only  when  cur- 
rent flows  through  its  coil.  When  the  current  is  stopped, 
the  iron  core  returns  almost  to  its  natural  state.  This  loss 
of  magnetism  is,  however,  not  absolutely  complete ;  a  very 
little  residual  magnetism  remains  for  a  longer  or  shorter  time. 
An  electromagnet  is  a  part  of  nearly  every  electrical 
machine,  including  the  electric  bell,  telegraph,  telephone, 
dynamo,  and  motor. 

To  determine  its  polarity,  we  shall  find  it  convenient  to  ex- 
press the  thumb  rule  as  us«d  for  a  straight  wire,  in  another 

way,  as  follows  :  - 

THUMB    RULE    FOR    A    COIL. 
Grrasp  the  coil  with  the  right  hand 
so  that  the  fingers  point  in  the  di- 
rection    of   the    current  in  the  coil, 
FIG.  235.  — Rule  for  polarity  of    and    the    thumb    will  point    to    the 

coil  carrying  current.  mrth  poU    Qj   ^    ^    (Fig>    235)> 

The  strength  of  an  electromagnet  depends  on  the  strength 
of  the  current  and  on  the  number  of  loops  or  turns  of  wire, 


MICHAEL  FARADAY.  Born  in  London,  in  1791,  the  son  of  a  blacksmith. 
Died  in  1867.  A  chemist  who  made  many  wonderful  discoveries  in  elec- 
tricity and  magnetism. 


JOSEPH  HENRY.  Born  in  Albany,  N.Y.,  in  1799.  Died  in  1878.  Was  for 
six  years  a  schoolmaster  at  Albany  Academy,  for  fourteen  years 
a  professor  at  Princeton,  and  for  the  rest  of  his  life  the  head  of  the 
Smithsonian  Institution  in  Washington.  Made  the  first  careful  study  of 
the  electromagnet,  and  shares  with  Faraday  the  honor  of  discovering 
the  laws  of  electromagnetic  induction. 


BATTERY  CURRENTS 


275 


It  is  the  practice,  in  order  to 
make  use  of  both  poles  of  an  elec- 
tromagnet, to  bend  the  iron  core 
and  the  coil  into  the  shape  of  a 
horseshoe,  as  shown  in  figure  236. 

Practical  electromagnets  were 
made  in  1831  by  Joseph  Henry, 
a  famous  American  schoolmaster 
and  scientist,  then  teaching  in  the 
academy  at  Albany,  N.Y.,  and 
by  Faraday  in  England.  Henry's 
magnet  was  capable  of  supporting 
fifty  times  its  own  weight,  which 
was  considered  very  remarkable 
at  the  time. 

Magnetic  hoists  are  now  built 
p 


FIG.  236.  —  Electromagnet. 


FIG.  237.  —  Electric-bell 
circuit. 


so  powerful  that  when  the  face  of  the 
iron  cores  is  brought  in  contact  with 
iron  or  steel  castings  and  the  current 
is  turned  on,  the  magnets  will  lift 
from  100  to  200  pounds  of  iron  per 
square  inch  of  pole  face,  and  yet  re- 
lease the  load  of  iron  the  moment  the 
current  is  cut  off. 

APPLICATIONS  OF  THE  ELECTRO- 
MAGNET 

269.  Electric  bell.  An  electric-bell 
circuit  usually  includes  a  battery  of 
two  or  more  cells,  a  push  button,  and 
connecting  wires,  besides  the  bell  itself 
(Fig.  237).  When  the  circuit  is  closed 
by  pushing  the  button  P,  the  current 
flows  through  the  electric  magnet  (rn) 
.and  attracts  the  armature  -4).  As 


276  PRACTICAL   PHYSICS 

the  armature  swings  to  the  left,  it  pulls  the  spring  (#)  away 
from  the  screw  contact  (J5)  and  breaks  the  circuit.  This 
stops  the  current,  and  the  electromagnet 
releases  the  armature.  It  then  springs 
back  again  and  closes  the  circuit  at 
the  screw,  and  the  whole  process  is  re- 
peated. The  swinging  of  the  armature, 
which  carries  a  hammer,  causes  a  series 
of  rapid  strokes  against  the  bell  as  long  as 
the  button  is  pushed.  It  does  not  mat- 
ter in  which  direction  the  current  flows. 
The  construction  of  the  push  button  P  is 

FIG.  238.-Push  button.  ,  figure 


270.  What  to  do  when  the  bell  won't  ring.    First  make  sure 
that  the  connecting  wires  at  the  bell,  push  button,  and  battery  are  firmly 
screwed  into  the  binding  posts. 

Next  inspect  the  battery.  The  liquid  should  fill  the  jar  within  an  inch 
of  the  top.  The  zinc  should  be  clean  and  free  from  crystals  and  should 
dip  into  the  solution,  but  should  not  touch  the  carbon. 

If  the  battery  consists  of  dry  cells,  you  will  do  well  to  get  a  pocket 
ammeter  and  try  each  cell.  A  new  cell  will  indicate  about  20  amperes. 
If  a  cell  has  dropped  much  below  5  amperes,  it  is  dead. 

Next  test  the  push  button  by  removing  the  cover  and  holding  a 
a  piece  of  metal  across  the  terminal  wires.  If  the  bell  rings,  it  shows 
that  the  trouble  is  a  poor  connection  in  the  button.  Brighten  up  the 
contact  points  with  sandpaper. 

Finally  look  over  the  bell  itself  carefully,  especially  the  point  where  the 
make  and  break  occurs.  Sometimes  the  screw  with  the  platinum  point 
gets  loose  or  gets  worn  off  and  needs  readjustment. 

271.  Telegraph.     The  word  "  telegraph  "  means  an  instru- 
ment which  "  writes  at  a  distance,"  for  the  early  forms  in- 
vented by  Samuel  F.  B.  Morse,  in   1844,  were  designed  to 
make  dots  and  dashes  on  a  moving  strip  of  paper,     Nowa- 
days the  receiving  instrument,  called  the  sounder,  makes  a 
series  of  clicks  separated  by  short  or  long  intervals  of  time 
to  represent  the  dots  and  dashes. 


BATTERY   CURRENTS 


277 


The  telegraph  consists  essentially  of  a  battery,  a  key,  and  a 
sounder,  as  shown  in  figure  239.     Gravity  cells  are  used  in 

.Key          Sounder  Sounder 

'itch 

fain  Hi 


Earth  Earth,. 

FIG.  239.  —  Simple  telegraph  circuit. 

practical  work,  but  for  experimental  purposes  any  kind  of 
battery  will  serve. 

The  key  (Fig.  240)  is  a  device,  something  like  a  push 
button,  for  making  and 
breaking  the  circuit.  The 
sounder  (Fig.  241)  consists 
of  an  electromagnet  with  a 
soft  iron  armature  which  is 
fastened  to  a  brass  bar.  This 


ADJUSTING  SCREWS 
CONTACT- 


BUTTON 


LEGJI 
FIG.  240.  — Telegraph  key. 


bar  is  pivoted  so  as  to  move 
up  and  down.  When  a  cur- 
rent flows  through  the  elec- 
tromagnet, the  armature  is  pulled  down ;  when  the  circuit 

is  broken,  a  spring  pulls  the 
bar  up  again.  Two  set  screws 
above  and  below  the  bar  limit 
its  motion  and  make  the  clicks. 
As  the  clicks  made  by  the  bar 
hitting  these  two  set  screws 
are  different,  the  ear  recog- 
nizes the  time  between  these 

FIG.  241. -Telegraph  sounder.          two  clicks    as   a   dot   Or   a    dash 

according  as  the  key  is  depressed  a  short  or  a  long  time. 

When    the  telegraph   came   into  commercial  use,  it   was 
found  that  the  resistance  of  the  connecting  wires,  called  the 


278 


PRACTICAL   PHYSICS 


line,  was  so  great  that  the  current  was  too  feeble  to  operate 
the  sounder,  even  when  many  cells  were  connected  in  series. 

A  relay  (Fig.  242)  is  there- 
fore employed  to  open  and 
close  the  circuit .  of  a  local 
battery  which  operates  the 
sounder.  This  relay  contains 
an  electromagnet  whose  coil 
has  many  turns  of  very  small 

FIG.  242.  —  Telegraph  relay.  T      f  t  ,,. 

copper  wire.     In  front  of  this 

magnet  is  a  light  iron  lever  which  is  held  away  from  the 
electromagnet  by  a  very  delicate  spring.  The  connections 
are  shown  in  figure  243.  When  the 
key  in  the  main  circuit  is  closed,  the 
weak  current  excites  the  relay  magnet 
enough  to  pull  the  armature  against  a 
set  screw,  thus  closing  the  local  circuit 
which  sends  a  strong  current  through 
the  sounder. 

In  ordinary  telegraphy  it  is  custom-  Local 
ary  to  use  a  single  wire  of  galvanized 
iron  or  hard-drawn  copper,  and  to  use 
the  earth  as  a  return  circuit.     At  each  Earth  •==- 

station  along  the  line  there  is  a  local  FlG-  -43-- Dia^am of  r* 

&  lay  telegraph  circuit. 

circuit    consisting     of      battery     and 

sounder,  which  is  closed  by  a  relay.  The  relay  is  in  another 
circuit  containing  a  key  and  the  main-line  battery  or  gen- 
erator. Each  key  is  provided  with  a  switch  so  that  the  main 
circuit  is  kept  closed  everywhere  except  at  the  station  where 
the  operator  is  sending  a  message. 

272.  Other  forms  of  telegraphs.  Through  the  inventions 
of  Edison  and  others  we  are  now  able  to  send  two  messages 
simultaneously  in  each  direction.  In  other  words,  we  can 
send  four  messages  over  a  single  wire  all  at  the  same  time. 
This  is  called  quadruplex  telegraphy. 


BATTERY  CURRENTS  279 

Submarine  telegraphy  began  as  early  as  1837,  but  it  was  not 
till  1866  that  a  really  successful  Atlantic  cable  was  laid. 
Such  a  cable  contains  a  central  conducting  core  of  copper 
wires  twisted  together.  This  is  surrounded  by  a  thick  in- 
sulating coating  of  rubber  and  outside  of  this  is  a  protective 
covering  of  hemp  and  steel  wires.  The  copper  core  and  the 
steel  sheath  act  like  the  coatings  of  an  immense  Leyden  jar. 
The  effect  of  this  is  to  make  the  sending  of  messages  very 
slow.  The  impulses  received  at  the  other  end  are  also  very 
weak.  It  was  only  when  an  exceedingly  delicate  receiving 
instrument  had  been  devised  by  Lord  Kelvin,  that  the  first 
Atlantic  cable  could  be  used  at  all. 

SUMMARY   OF   PRINCIPLES   IN   CHAPTER   XV 

Current  flows  downhill,  from  4-  to  — ,  in  outside  circuit. 
Current  is  pumped  uphill,  from  —  to  -f-,  inside  of  cell. 

Energy  is  supplied  by  chemical  action  of  acid  on  zinc. 
Zinc  is  fuel  of  cell. 

Current  carried  through  cell  by  charged  ions  (pieces  of  molecules). 

Lines  of  magnetic  force  around  a  straight  current  are  concentric 

circles. 

Thumb  rule  for  straight  wire:  Use  right  hand.     Thumb  points 
with  current.    Fingers  curl  with  field. 

Lines  of  force  around  a  coil  mostly  go  through  inside  and  come 

back  outside. 

Thumb  rule  for  coil:  Use  right  hand.     Thumb  points  with  field 
toward  AT-pole.    Fingers  curl  with  current. 

QUESTIONS 

1.  An  electromagnet  is  found  to  be  too  weak  for  the  purpose  intended. 
How  may  its  strength  be  increased? 

2.  In  looking  at  the  TV  end  of  an  electromagnet,  in  which  direction 
does  the  current  go  around  the  core,  clockwise  or  anticlockwise  ? 


280  PRACTICAL  PHYSICS 

3.  If  you  find  that  the  JV-pole  of  a  compass  held  under  a  north  and 
south  trolley  wire  points  toward  the  east,  what  is  the  direction  of  the 
current  in  the  wire? 

4.  In  a  certain  factory,  steel  was  once  used  by  mistake  instead  of  soft 
iron  to  make  the  cores  of  the   electromagnets   for   some   bells.     What 
would  be  the  matter  with  the  bells? 

5.  What  would  be  the  effect  of  winding  an  electromagnet  with  bare 
copper  wire  instead  of  insulated? 

6.  What  sort  of  material  is  used  to  insulate  copper  wire  which  is  to 
be  used  («)  to  wind  electromagnets,  (6)  to  wire  electric  doorbell  circuits, 
and  (c)  for  electric  lights? 

7.  What  is  the  difference  between  a  relay  and  a  sounder  that  makes 
it  possible  for  a  weak  current  to  work  one  and  not  the  other? 


CHAPTER  XVI 
MEASURING  ELECTRICITY 

Galvanometers  —  the  ampere  —  ammeters  —  the  ohm  —  in- 
ternal and  external  resistance — the  volt  —  voltmeters. 

Ohm's  law  for  whole  circuit  and  for  part  of  circuit  —  resist- 
ances in  series  and  in  parallel  —  cells  in  series  and  in  parallel. 

Specific  resistance  and  the  circular  mil  —  effect  of  tempera- 
ture on  resistance  —  resistance  boxes  —  measurement  of  resis^t- 
ance  by  voltmeter-ammeter  method,  and  by  Wheatstone  bridge. 

273.  Necessity  for  a  unit  of  current  strength.     In  the  con- 
struction, study,  and  use  of  electrical  machinery,  we  are  con- 
stantly dealing  with  electric  currents.     We  say  a  current  is 
strong  or  weak,  just  as  we  speak  in  a  rough  way  of  things 
being  fast  or  slow,  hot  or  cold.     When,  however,  we  go  a 
step  farther  and  ask  how  strong  this  current  is  or  how  weak 
that  current  is,  we  are  forced  to  have  some  unit  of  current 
strength,  and  some  means  of  measuring  currents  in  terms 
of  it. 

274.  Galvanometers.  —  We  can  get  an  idea  of  the  relative 
strength  of  two  currents  by  means  of  a  galvanometer.     There 
are  two  kinds  of  galvanometers  in  common  use,  the  older  of 
which  is  the  moving-magnet  galvanometer  (Fig.  244).     This 
consists  of  a  compass  needle  pivoted  or  hung  at  the  center 
of  a  large  wooden  frame  on  which  are  wound  one  or  more 
turns  of  wire.     This  coil  is  set  facing  east  and  west  so  that 
the  compass  needle  lies  parallel  to  its  plane.      When  a  cur- 
rent is  sent  through  the  wire,  an  east  and  west  magnetic  field 
is  set  up  at  the  center  of  the  coil  and  the  compass  is  deflected 
more  or  less  according  as  the  current  is  stronger  or  weaker. 

281 


282 


PRACTICAL.  PHYSICS 


In  the  type   of  galvanometer  just  described,  the  coil  is 
large  and  is  fastened  firmly  to  the  base,  while  the  magnet  is 


FIG.  244.  —  Moving-magnet  galvanometer  and  diagram  of  essential  parts. 

small  and  movable.     In  the  moving-coil  type  (Fig.  245),  the 
magnet  is  large  and  is  fastened  firmly  to  the  base,  while  the 

coil  is  small  and  movable.  The 
magnet,  NS,  is  usually  made  in  the 
shape  of  a  horseshoe  so  that  it  may 
be  as  strong  as  possible.  The  coil  is 
wound  on  a  very  light  rectangular 
frame  and  hangs  between  the  jaws 
of  the  magnet.  Usually  there  is 
a  cylinder,  I,  of  soft  iron  in  the 
space  inside  the  moving  frame  to 
still  further  increase  the  field. 
The  bottom  of  the  coil  is  con- 
nected with  a  binding  post,  B,  by 
a  spiral  of  very  fine  wire  which 
carries  the  current  into  the  coil 
without  disturbing  its  freedom  to 
rotate ;  the  current  leaves  the  coil 
through  the  fine  suspension  wire,  AC.  The  top  of  this  wire 
is  twisted  until  the  coil  hangs  in  the  plane  of  the  poles  N 


FIG.  245.  —  Moving-coil  galva- 
nometer and  diagram  of  essen- 
tial parts. 


MEASURING  ELECTRICITY  283 

and  S  when  no  current  is  passing  through  it.  If  there  is  a 
current,  the  coil  acts  like  a  tiny  magnet  with  poles  pointing 
to  the  front  and  rear,  and  tries  to  turn  itself  so  that  these 
poles  may  get  as  near  possible  to  the  .2V  and  S  poles  of  the 
magnet.  The  amount  by  which  it  is  able  to  twist  the  sus- 
pension wire  measures  the  current. 

The  moving-coil  type  is  much  more  convenient  for  ordi- 
nary work,  but  the  moving-magnet  type  can  be  made  much 
more  sensitive,  and  is  used  when  very  small  currents  have  to 
be  detected  or  measured. 

275.  The  ampere.  Having  learned  how  to  compare  cur- 
rents by  means  of  a  galvanometer,  let  us  consider  what  the 
unit  is,  in  terms  of  which  currents  can  be  measured.  When 
we  open  the  faucet  at  a  sink,  a  current  of  water  flows  through 
the  pipe.  The  rate  of  this  flow  can  be  easily  measured  in 
cubic  feet  (or  gallons)  of  water  per  minute  (or  per  second). 
Thus  we  speak  of  water  as  flowing  at  the  rate  of  1  gallon  per 
second  or  5  gallons  per  second.  In  much  the  same  way  we 
speak  of  electricity  as  flowing  along  a  wire  at  the  rate  of  1 
coulomb  per  second  or  5  coulombs  per  second.  The  coulomb 
is  the  unit  quantity  of  electricity,  just  as  the  gallon  is  the 
unit  quantity  of  water.  We  have  to  consider  the  rate  of 
flow  of  electricity  so  often  that  we  have  a  special  name  for 
the  unit  rate  of  flow,  1  coulomb  per  second.  We  call  it  an 
ampere.  Thus  5  amperes  means  5  coulombs  per  second. 

It  is  possible  to  define  the  ampere  in  terms  of  the  magnetic 
effect  of  an  electric  current,  but,  as  a  matter  of  fact,  electrical 
engineers  have  agreed  to  define  the  ampere  in  terms  of  its 
chemical  effect.  If  two  silver  (Ag)  plates  are  placed,  in  a 
jar  of  silver  nitrate  solution  (AgNO3),  and  if  the  +  and  - 
terminals  of  a  battery  are  connected,  one  to  one  plate  and  one 
to  the  other,  it  will  be  found  that  the  plate  where  the  current 
goes  in  (the  anode)  loses  in  weight  because  silver  is  dissolved, 
and  the  plate  where  the  current  comes  out  (the  cathode)  gains 
in  weight  because  silver  is  deposited.  By  international  agree- 


284 


PRACTICAL  PHYSICS 


ment  the  quantity  of  electricity  which  deposits  0.001118  grams 
of  silver  is  one  coulomb,  and  the  current  which  deposits  silver 
at  the  rate  of  0.001118  grams  per  second 
is  one  ampere.  The  apparatus  used  in 
the  accurate  measurement  of  current 
by  this  method  is  shown  in  figure  246. 
The  anode  is  the  silver  disk  at  the  left, 
and  the  cathode  is  the  silver  (or  plati- 
num) cup  at  the  bottom.  The  porous 
cup  at  the  right  is  put  between  the 
anode  and  the  cathode  in  the  solution 
like  the  cup  in  a  Daniell  cell. 

276.   Illustrations  of  the  ampere.  When 

FIG.  246.  -  Silver  coulomb-    a  ne w  dr^  cel1  is  short-circuited  with  a  short  stout 

meter.  wire,  about  20  amperes  flow  through  the  wire. 

An  ordinary  16  candle  power  carbon  filament 

electric  lamp  takes  a  little  less  than  half  an  ampere,  while  the  arc  lamps 
used  for  street  lighting  require  from  6  to  10  amperes.     A  telegraph  sounder 
operates  on  0.25  amperes,  and  a  telephone  receiver  on  less  than  0.1  am- 
peres, while  the  motor  on  a  street  car 
often  takes  as  much  as  40  or  50  amperes. 


277.  The  ammeter.  The  legal 
method,  described  above,  of  defin- 
ing an  ampere  is  not,  of  course,  a 
convenient  method  of  measuring 
current  strength.  The  coulomb- 
meter  is  used  only  for  standardiz- 
ing the  ammeters  which  are  used 
in  everyday  life  to  indicate  cur- 
rent strength. 

The  commercial  ammeter  (ampere- 
meter) is  a  shunted,  moving  coil  gal- 
vanometer. The  instrument  (Fig. 

247)  contains  a  coil  of  fine  insulated  copper  wire,  wound  on 
a  light  frame,  and  mounted  in  jeweled  bearings  between  the 


FIG.  247.  — Ammeter. 


MEASURING  ELECTEICITT  285 

poles  of  a  strong  permanent  horseshoe  magnet.  A  fixed  soft 
iron  cylinder  midway  between  the  poles  of  the  magnet  concen- 
trates the  field.  The  moving  coil  rotates  in  the  gap  between 
the  core  and  the  pole  pieces.  The  coil  is  held  in  equilibrium 
bv  two  spiral  springs,  which  serve  also  to  carry  the  current 
into  and  out  from  the  coil.  Only  a  small  fraction,  perhaps 
0.001  of  the  current  to  be  measured,  goes  through  the  mov- 
able coil,  the  major  part  being  carried  past  the  coil  by  a 
metal  strip  called  a  shunt.  Since  the  current  through  the 
coil  is  a  constant  fraction  of  the  whole  current,  the  pointer 
which  is  attached  to  the  moving  coil  can  be  made  to  indicate 
directly  on  a  graduated  scale  the  number  of  amperes  in  the 
total  current. 

It  will  be  seen  that  the  resistance  of  an  ammeter,  which  is 
practically  the  resistance  of  the  shunt,  is  very  small,  and  that 
the  whole  current  passes  through  the  instrument. 

278.  Electrical  resistance.  Although  we  divide  substances 
into  two  classes,  conductors  and  non-conductors  or  insu- 
lators, yet  even  the  best  conductors  of  electricity  are  not 
perfect.  This  means  that  all  conductors  offer  some  resistance 
to  the  flow  of  electricity  and  transform  a  part  of  the  energy 
which  they  carry  into  heat.  We  are  already  familiar  with 
the  fact  that  a  stream  of  water  flowing  through  a  pipe  is 
held  back  or  retarded  by  the  friction  of  the  pipe.  The 
amount  of  this  friction  depends  on  the  smoothness  of  the 
inner  surface,  the  length  and  the  size  of  the  pipe.  So  with 
electricity,  the  resistance  of  a  conductor  depends  :  — 

(1)  On  the  material  used ;  iron,  for  example,  has  nearly  7 
times  as  much  resistance  as  copper ; 

(2)  On  the  length ;  a  wire  10  feet  long  has  twice  as  much 
resistance  as  a  wire  5  feet  long ; 

(3)  On  the  size  of  the  wire  ;  a  wire  0.04  inches  in  diameter 
has  one  fourth  the  resistance  of  a  wire  0.02  inches  in  diameter  ; 

(4)  On  the  temperature  ;   heating  a  copper  wire  from  0°  to 
100°C  increases  its  resistance  about  40%. 


286  PRACTICAL   PHYSICS 

279.  Legal  ohm,  the  unit  of  resistance.     The  legal  unit  of 
resistance,  called  the  ohm,  is  the  resistance  at  0°  C  of  a  column 
of  mercury  106.3  centimeters  long,  with  a  cross  section  of 
about  1  square  millimeter  (more  exactly,  of  uniform  cross 
section  and  weighing  14.4521  grams).     This  legal  definition 
of  the  ohm  fixes  the  material,  length,  cross  section,  and  tem- 
perature of  the  conductor  whose  resistance  is  taken  as  the 
standard.     Since  a  column  of  mercury  is  not  convenient  to 
handle,  we   ordinarily  use   "standard   coils"  made   of  some 
high-resistance  alloy,  such  as  German  silver  or  manganin. 

280.  Illustrations  of  the  Ohm.     About  157  feet  of  #  18  copper  wire 
(the  size  ordinarily  used  to  connect  electric  bells),  or  26  feet  of  iron  wire 
or  6  feet  of  manganin  wire  of  the  same  size,  has  a  resistance  of  1  ohm. 
The  resistance  of  a  small  electric  bell  is  about  3  ohms,  of  a  telegraph 
sounder  4  ohms,  of  a  relay  200  ohms,  of  a  telephone  receiver  60  ohms, 
and  of  16  candle  power  incandescent  lamp  220  ohms  when  hot. 

281.  Internal  and  external  resistance.     It  must  not  be  for- 
gotten that  there  is  resistance  to  the  flow  of  electricity  in 
every  part  of  an  electric  circuit.     In  the  case  of  the  electric- 
bell  circuit,  there  is  the  bell  itself,  the  push  button,  the  con- 
necting  wires,   and    the    battery.      The    resistance    of   the 
generator,  whether  it  be  a  battery  or  a  dynamo,  is  called 
the  internal  resistance,  and  that  of  the  rest  of  the  circuit  is  the 
external  resistance.     It  is  the  gradual  increase  in  the  internal 
resistance  of  a  long-used  dry  cell  which  cuts  down  the  cur- 
rent it  can  deliver  and  so  destroys  its  usefulness. 

282.  Electromotive  force.     In  hydraulics  we  know  that  to 
get  water  to  flow  along  a  pipe  it  is  essential  to  have  some 
driving  or  motive  force,  such  as  that  furnished  by  a  pump. 
In  much  the  same  way,  to  get  electricity  to  flow  along  a  wire 
we  must  have  an  electromotive  force,  such  as  that  furnished  by 
a  battery  or  dynamo.     The  unit  of  electromotive  force  is  the 
volt.     A  volt  may  be  defined  as  the  electromotive  force  needed  to 
drive  a  current  of  one  ampere  through  a  resistance  of  one  ohm. 


MEASURING  ELECTRICITY  287 

283.  Illustrations  of  VOlts.     A  common  dry  cell  gives  about  1.4 
volts,  and  a  storage  cell  about  2  volts.     A  gravity  cell  gives  about  1.08 
volts,  and  the  so-called  Weston  Standard  cell,  used  in  very  exact  voltage 
measurements,  gives  1.0183  volts  at  20°  C.     The  current  for  lighting  a 
building  is  usually  delivered   at   110  or  220  volts,  and  street  cars  op- 
erate on  about  550  volts. 

284.  Distinction  between  volts  and  amperes.     The  intensity 
of  an  electric  current  is  measured  in  amperes,  the  electromotive 
force  driving  the  current  is  measured  in  volts.     In  a  given  cir- 
cuit the  greater  the  electromotive  force  is,  the  greater  is  the 
current.      We  know  that  we  must  have  a  certain  "  head  "  of 
water  in  order  to  get  a  given  number  of  gallons  of  water  to 
flow  through  a  given  pipe  each  second ;    so  we  must  have  a 
certain  electromotive  force  to  make  a  given  current  of  elec- 
tricity flow  through  a  given  wire.     With  both  water  and 
electricity  we  must  have  a  motive  force  in  order  to  have  a 
current,  but  we  may  have  the  motive  force  and  yet  have  no 
current.     If  the  valve  is  closed  in  the  water  pipe  or  the 
switch  is  open  in  the  electric  circuit,  we  might  have  motive 
force  (volts)  but  no  current  (amperes). 

COMPARISON  OF  HYDRAULIC  AND  ELECTRICAL  UNITS 

UNITS  WATER                           ELECTRICITY 

Quantity  Gallon  Coulomb 

Current  Gallon  per  sec.  Ampere  =  1  coulomb  per  sec. 

Motive  force  "  Feet  of  head  "  Volt 

Resistance  Ohm 

285.  The  voltmeter.     The  commercial  voltmeter  is  simply  a 
high-resistance  galvanometer.     When   electromotive  force   is 
applied  to  a  galvanometer,  the  current  it  allows  to  pass  is 
proportional  to  the  voltage,  and  so  the  scale  can  be  gradu- 
ated  to  read  the  voltage  directly.     The  instrument    (Fig. 
248)  is  usually  a  moving  coil  galvanometer,  like  an  ammeter. 
Indeed  the  same  instrument  is  often  used  for  both  purposes. 
A  voltmeter  does  not  have  a  shunt  between  its  terminals, 


288 


PRACTICAL  PHYSICS 


FIG.  248.  —Voltmeter. 


like  an  ammeter,  but  does  have  a 
large  resistance  coil  inserted  in  se- 
ries, so  that  only  a  very  small  cur- 
rent passes  through  the  instrument, 
but  all  of  it  goes  through  the  mov- 
ing coil.  In  fact  such  a  voltmeter 
gives  correct  values  only  when  the 
current  used  is  so  small  as  not  to 
affect  appreciably  the  voltage  to  be 
measured. 

This  will  be  understood  by  considering 
the  water  analogy  shown  in  figure  249.     It 

is  evident  that  the  current  in  the  connecting  pipe  AB  is  a  good  measure 
of  the  difference  in  level  between  L  and  L',  only  when  the  current  in  AB 
is  so  small  as  not  to  change  appreciably  the 
levels  whose  difference  is  to  be  measured. 

To  make  voltmeters  usable  over  dif- 
ferent ranges  we  have  merely  to  con- 
nect coils  of  different  resistance  in 
series  with  the  same  galvanometer. 

Since  the  voltmeter  is  an  instrument 
for  measuring  the  electromotive  force 
between  the  two  ends  of  a  circuit  or  of 
part  of  a  circuit,  it  must  have  its  ter- 
minals Connected  to  the  two  points;  FIG.  249.  —  Water  analogue 

that  is,  it  mu§t  be  put  across  the  circuit, 

not  in  it.     The  proper  connections  for  both  ammeter  and 

voltmeter  are  shown  in  figure  250. 

286.  Electromotive  force  of  a  cell. 

If  the  electromotive  force  of  a  simple  cell  is 
observed  with  a  voltmeter,  it  will  be  found 
that  the  voltage  of  the  cell  is  not  changed 
by  moving  the  plates  near  together  or  far 
apart,  or  by  lifting  them  almost  out  of  the 
liquid  so  as  to  change  greatly  their  effective 
size.  These  changes  affect  the  current  sent  by  the  cell  through  an  ex- 
ternal circuit  by  changing  the  internal  resistance  of  the  cell,  not  its  voltage. 


w 


FIG.  250.  — How  to  connect  a 
voltmeter  and  ammeter. 


MEASURING  ELECTRICITY  289 

If  a  stick  of  carbon  is  used  instead  of  a  copper  plate,  the  voltage  of 
the  cell  will  be  found  to  be  greater;  if,  however,  hydrochloric  acid  is 
used  instead  of  sulphuric,  the  voltage  is  less. 

All  this  shows  that  the  voltage  of  a  cell  depends,  not  on 
its  size,  but  on  the  materials  of  which  it  is  made.  A  very 
large  storage  cell  with  plates  several  square  feet  in  area,  such 
as  is  used  in  power  stations,  gives  exactly  the  same  2  volts 
that  a  tiny  cell  in  a  test  tube  would  if  made  of  the  same 
materials.  The  large  cell  can  drive  more  current  through  a 
given  circuit  than  a  small  one  because  its  internal  resistance 
is  so  small.  Of  course,  with  constant  use,  the  small  cell 
would  be  exhausted  much  more  quickly. 

287.  Ohm's  law.  Let  a  Daniell  cell  be  connected  in  series  with  a 
considerable  resistance,  perhaps  100  ohms,  and  a  galvanometer,  and  the 
current  noted.  If  two  cells  are  used  in  series,  the  current  will  be  about 
twice  as  great.  If,  without  changing  the  number  of  cells,  we  double  the 
external  resistance,  the  current  will  be  about  half  as  great.  If  we  halve 
the  external  resistance,  the  current  will  be  doubled. 

In  general,  we  find  that  the  current  increases  as  the 
electromotive  force  increases,  and  that  the  current  decreases 
as  the  resistance  in  the  circuit  increases.  A  German  physi- 
cist, Ohm  (1789-1854),  was  the  first  to  state  this  relation 
between  current,  electromotive  force,  and  resistance.  The 
law  is :  The  intensity  of  the  electric  current  along  a  conductor 
equals  the  electromotive  force  divided  by  the  resistance. 

Current  =  electromotive  force 

resistance 
In  electrical  units:  — 

volts 


In  symbols :  — 


Amperes 

ohms 


/=! 

1    R' 


where  1=  Intensity  of  current  in  amperes, 

E  —  Electromotive  force  in  volts, 
R  =  Resistance  in  ohms. 


290  PRACTICAL  PHYSICS 

If  we   know   the    current  and    resistance    and    want   the 
electromotive  force,  we  have 


If  we  know  the  electromotive  force  and  current  and  want 
to  calculate  the  resistance,  we  have 

..*. 

288,   Examples  using  Ohm's  law. 

1.  What  is  the  intensity  of  the  current  sent  through  a  resistance  of 
5  ohms  by  an  electromotive  force  of  110  volts? 

/  =  E.  =  115  =  22  amperes. 
R       5 

2.  What   electromotive   force  is  needed   to   send  a  current  of  0.03 
amperes  through  a  resistance  of  1000  ohms  ? 

E  =  IR  =  0.03  x  1000  =  30  volts. 

3.  Through   what   resistance   will   110  volts   send   a  current   of   10 
amperes  ? 

fl  =  *?  =  !!?  =  11  ohms. 

PROBLEMS 

1.  Find  the  intensity  of  the  current  which  an  electromotive  force  of 
10  volts  sends  through  a  resistance  (a)  of  3  ohms,  (b)  of  40  ohms. 

2.  How  much  electromotive  force  is  needed  to  send  2  amperes  through 
(a)  2  ohms,  (&)  50  ohms  ? 

3.  What  is  the  resistance  of  a  circuit  when  the  electromotive  force  is 
110  volts  and  the  current  intensity  is  2  amperes  ? 

4.  An   electric   heater  of   10  ohms    resistance   can  safely   carry  12 
amperes.     How  high  can  the  voltage  run? 

5.  An  .electromagnet  draws  4  amperes  from  a  110-volt  line.     How 
much  would  it  draw  from  a  220-volt  line  ? 

6.  A  certain  dry  cell  has  an  electromotive  force  of  1.5  volts  and  will 
give    about  27   amperes   when   short-circuited.     What   is    its    internal 
resistance?     What  is  the  internal  resistance  of  the  same  cell  when,  after 
much  use,  it  will  give  only  9  amperes  ? 


Button 


MEASURING  ELECTRICITY  291 

289.  Application  of  Ohm's  law  to  partial  circuits.     Not  only 
does  Ohm's  law  apply  to  an  entire  circuit,  the  current  in  the 
entire  circuit  being  equal  to  the  total  electromotive   force 
divided  by   the  resistance  of  the  entire  circuit,  but  it  also 
applies  to  any  part  of  a  circuit. 

That  is,  the  current  in  a  certain  Ben 

part  of  a  circuit  equals  the  volt- 
age  across  that  same  part  divided 
by  the  resistance  of  the  part. 

For  example,  suppose  the  electromo- 
tive force  of  a  battery  is  3  volts,  the  re- 
sistance of  the  bell  (Fig.  251)  is  3  ohms,  Battery 

the  resistance  of  the  wires  and  button  is  fio.  251.  —  Bell  circuit. 

1.5  ohms,  and  the  internal  resistance  of 
the  battery  is  0.5  ohms.  To  find  the  intensity  of  the  current,  we  have 

-El  Q 

I  =  —  =  -  =  0.6  amperes. 
R      3+1.5  +  0.5 

The  current  has  the  same  intensity  throughout  the  circuit.     To  find  the 
voltage  across  the  bell,  we  have 

E  =  IR  =  0.6  x  3  =  1.8  volts. 

To  find  the  voltage  drop  within  the  battery,  we  have 
E  =  IR  =  0.6  x  0.5  =  0.3  volts. 

Since  the  total  electromotive  force  of  the  battery  is  3  volts,  and  it 
takes  0.3  volts  to  send  the  current  through  the  battery  itself,  the  terminal 
voltage  of  the  battery  is  3  -  0.3,  or  2.7  volts.  Of  this  1.8  volts  is  needed 
to  send  the  current  through  the  bell  and  the  remainder,  0.9  volts,  is  used 
to  send  the  current  through  the  connecting  wires  and  push  button. 

If  a  voltmeter  were  connected  across  the  battery,  it  would  read  2.7 
volts,  or  the  terminal  voltage.  The  total  electromotive  force  (e.  m.  f.)  is 
computed  by  multiplying  the  current  in  the  circuit,  0.6  amperes,  by  the 
total  resistance,  3  +  1.5  +  0.5  =  5  ohms. 

E  =  IR  =  0.6  x  5  =  3.0  volts  total  e.  m.  f  . 

3.0  -  0.3  =  2.7  volts  terminal  voltage. 

290.  Terminal  voltage  of  a  cell  depends   on  its  current. 

Connect  a  voltmeter  to  the  terminals  of  a  dry  cell,  and  note  the  e.  m.  f. 
Then  connect  a  coil  of  very  high  resistance  (1000  ohms)  across  the  ter- 


292  PRACTICAL  PHYSICS 

minals.  The  terminal  voltage,  as  indicated  by  the  voltmeter,  is  very 
nearly  the  same  as  before.  But  if  we  connect  a  short,  thick  wire 
across  the  terminals,  so  as  to  draw  a  large  current,  we  see  by  the  volt- 
meter that  the  terminal  voltage  drops  instantly. 

Thus  we  see  that  the  voltage  drop  in  a  cell  depends  di- 
rectly upon  the  current  used,  and  that  the  terminal  voltage 
decreases  when  the  current  increases. 

291.  Series  arrangement.  Let  us  consider  still  further 
the  electric  current  in  apparatus  arranged  in  series. 

A      B  c 

6  ohms.  3  ohms.  1.5  ohms. 

123 
1 1 ll— ll 


0.5         0.5         0.5 

Battery 
FIG.  252.  — Three  cells  and  three  resistances  in  series. 

In  figure  252  we  have  three  cells  and  three  resistances  connected  in 
series.  By  this  we  mean  that  the  carbon  of  cell  3  is  joined  to  the  zinc 
of  cell  2,  and  the  carbon  of  cell  2  is  joined  to  the  zinc  of  cell  1.  The 
circuit  then  runs  from  the  carbon  of  cell  1  through  the  resistances  A,  B, 
and  C  in  succession,  back  to  the  zinc  of  cell  3. 

The  laws  governing  series  circuits  are  as  follows:  — 

The  current  in  every  vart  of  a  series  circuit  is  the  same. 

The  resistance  of  several  resistances  in  series  is  the  sum  of  the 
separate  resistances. 

The  voltage  across  several  resistances  in  series  is  equal  to  the 
sum  of  the  voltages  across  the  separate  resistances. 

Moreover,  since  the  voltage  is  equal  to  the  resistance  times 
the  current  (jBr=ZZ2),  and  since  the  current  (/)  in  every 
part  of  a  series  circuit  is  the  same,  it  follows  that  the  voltage 
across  any  part  of  a  series  circuit  is  proportional  to  the  resist- 
ance of  that  part. 

For  example,  in  figure  252,  if  the  e.  m.  f .  of  each  cell  is  2  volts,  the 
e.  m.  f.  of  the  three  cells  in  series  is  3  times  2,  or  6  volts. 


MEASURING  ELECTRICITY 


293 


If  the  resistance  of  A  is  6  ohms,  of  B,  3  ohms,  of  C,  1.5  ohms,  and  of 
each  cell,  0.5  ohms,  the  total  resistance  is  6  +  3  + 1.5  +  (3  x  0.5)  =  12 
ohms. 

The  current  is  T62,  or  0.5  amperes. 

The  voltage  across  A  is  6  times  0.5,  or  3  volts,  across  B,  3  times  0.5, 
or  1.5  volts,  and  across  C,  1.5  times  0.5,  or  0.75  volts. 

The  voltage  "  drop  "  in  each  cell  is  0.5  times  0.5,  or  0.25  volts,  so  that 
the  terminal  voltage  of  each  cell  is  2  —  0.25,  or  1.75  volts. 

292.  Parallel  arrangement.  When  the  several  resistances 
are  so  arranged  that  the  current  divides  between  them,  as 
shown  in  figure  253,  part 
going  through  A,  part 
through  B,  and  the  rest 
through  (7,  they  are  said 
to  be  in  parallel  or  multiple 
or  shunt. 

The  voltage  across  each 

12  volts 


1  amp. 


Y  .6  amps. 


FIG.  253.  —  Three  resistances  in  parallel. 


/ 
"7  ^ 

)' 

7  1 
* 


separate  resistance  of  the 

three  parallel  resistances 

is  the  same.     For  example,  if  the  voltage  across  A  is  12  volts, 

then  the  voltage  across  B  is  12  volts,  and  also  across  (7,  for 

each  resistance  lies  between  the  same  two  points,  X  and  Y. 

The  currents,  however,  in  each  of  the  resistances  in  parallel 
are  not  the  same,  unless  the  resistances  are  all  equal.  If,  for 
example,  the  resistances  of  A,  B,  and  0  are  each  6  ohms,  the 
current  in  each  is  2  amperes.  But  if  the  resistances  are 
unequal,  the  greatest  current  will  flow  through  the  smallest 
resistance.  Of  course  the  total  current  passing  through  a 
parallel  arrangement  of  resistances  is  equal  to  the  sum  of  the 
currents  in  the  separate  conductors.  Thus  if  the  current  in 
A  is  1  ampere,  in  B,  2  amperes,  and  in  (7,  3  amperes,  the  total 
current  through  the  combination,  and  through  the  rest  of 
circuit,  is  1  +  2  +  3,  or  6  amperes. 

293.  Calculation  of  resistances  in  parallel.  If  we  know  the 
voltage  and  total  current  through  a  set  of  resistances  in 
parallel  we  have  merely  to  apply  Ohm's  law  to  compute  the 


294  PRACTICAL  PHYSICS 

total  resistance  of  the  combination.  Thus,  if  the  voltage 
across  A,  B,  and  (7  in  figure  253  is  12  volts,  and  the  total 
current  is  6  amperes,  the  total  resistance  is  2  ohms. 

In  case  we  know  only  the  separate  resistances  and  want  to 
compute  their  combined  resistance  in  parallel,  we  may  well 
make  use  of  the  idea  of  conductance.  By  conductance  we 
mean  the  ease  with  which  a  current  flows  along  a  wire,  while 
resistance  represents  the  difficulty. 

Conductance  is  the  reciprocal  of  resistance ;  that  is, 

4 

Conductance  = 


resistance' 

The  unit  of  conductance  is  the  mho,  which  is  the  unit  of 
resistance  (ohm)  spelled  backwards. 

4 

1  mho  = 


1  ohm 

Thus  a  wire  has  a  conductance  of  1  mho  when  its  resistance  is  1  ohm, 
and  a  conductance  of  2  mhos  when  the  resistance  is  0.5  ohms. 

It  can  be  easily  shown  that  the  conductance,  of  a  parallel 
arrangement  is  equal  to  the  sum  of  the  conductances  of  the 
separate  parts. 

Thus  suppose  three  resistances,  A,  B,  and  (7,  are  arranged  in  parallel 
and  are  12,  6,  and  4  ohms  respectively.  Find  their  combined  resistance. 

Let  R  =  resistance  of  A,  B,  and  C  in  parallel. 

Then  JTH+J  +  i- 

Whence  R  =  2  ohms. 

294.  Cells  arranged  in  parallel.  Not  only  may  the  separate 
external  resistances  be  arranged  in  parallel,  but  the  cells  or 
generators  themselves  may  be  so  arranged.  For  example,  in 
figure  254  we  have  a  battery  of  three  cells  arranged  in 
parallel. 


MEASURING  ELECTRICITY  295 

The  laws  governing  such  a  case  are  as  follows :  — 

The  voltage  of  the  battery  is  the  voltage  of  one  cell. 

The  internal  resistance  of  the  battery  is  the  resistance  of  one 
cell  divided  by  the  number  of  cells,  since  three  cells*  R 

for  example,  have  three  times  the  conductance  of 
one  cell. 

The  current  will  be  the  sum  of  the  currents 
through  each  cell. 

*         ?2 
For  example,  suppose  that  in  figure  254  the      t 

voltage  of  each  cell  is  2  volts,  the  resistance  of      e 
each  cell  is  0.6  ohms,  and  the  external  resist- 
ance U  is  0.3  ohms,  and  we  desire  to  find  the  FIG.  254.— Three 
current  through  each  cell.  8  in  paraUeL 

The  total  current  Jis  found  by  Ohm's  law;  thus 

E  2  2 

/  =  -p  =  -     — ^— 7  =  -^  =  4  amperes. 


Then  the  current  in  each  cell  will  be  \  of  4  amperes  or 
1.3  amperes. 

295.  Best  arrangement  of  cells  of  a  battery.  By  means  of  a 
lecture  table  voltmeter  we  may  show  that  the  e.  ra.  f.  of  6  cells  in  series  is 
6  times  that  of  one  cell,  and  that  the  e.  m.f.  of  6  cells  in  parallel  is  the 
same  as  that  of  one  cell. 

By  using  an  ammeter  and  a  small  external  resistance,  we  can  show 
that  6  cells  arranged  in  parallel  give  more  current  than  6  cells  in  series; 
but  with  considerable  external  resistance,  the  series  arrangement  fur- 
nishes the  greater  current. 

In  general,  to  make  the  intensity  of  the  current  as  large 
as  possible,  when  the  external  resistance  is  large,  arrange  the 
cells  in  series,  but  when  the  external  resistance  is  small,  arrange 
the  cells  in  parallel. 

We  can  easily  see  the  reason  for  this  if  we  recall  from  the 
foregoing  discussion  that  in  a  series  battery  the  voltage  and 


296  PRACTICAL  PHYSICS 

the  internal  resistance  of  each  cell  are  both  multiplied  by  the 
number  of  cells.  In  the  parallel  arrangement  of  cells  the 
voltage  is  not  increased,  and  the  internal  resistance  of  each 
cell  is  divided  by  the  number  of  cells.  From  Ohm's  law 
we  have 


where  R  is  the  external  resistance  and  r  the  internal.  If  R 
is  much  larger  than  r,  it  does  not  make  much  difference  just 
how  large  r  is,  and  we  should  make  E  as  large  as  possible  by 
arranging  the  cells  in  series.  But  if  R  is  small,  r  becomes 
the  important  part  of  the  denominator,  and  it  pays  to  make 
r  as  small  as  possible  by  arranging  the  cells  in  parallel. 

In  practical  work  the  external  resistance  is  usually  large 
compared  with  the  internal  resistance,  so  the  cells  of  a 
battery  are  generally  arranged  in  series. 

PROBLEMS 

1.  Three  resistances,  A  =  80  ohms,  R  =  60  ohms,  and  C  =  40  ohms, 
are  put  in  parallel  and  the  voltage  across  the  combination  is  120  volts. 
Find  the  current  in  each,  the  total  current,  and  the  resistance  of  the 
combination. 

2.  If  a  battery  is  used  to  light  20  lamps  arranged  in  parallel,  and 
each  lamp  requires  0.5  amperes,  how  many  amperes  must  the  battery 
supply  ? 

3.  What  e.  m.  f.  will  be  needed  to  force  2  amperes  through  a  series 
circuit,  containing  a  battery  of  resistance  £  ohm,  a  line  of  resistance  1 
ohm,  and  a  lamp  of  resistance  100  ohms? 

4.  Three  lamps  of  150  ohms  each  are  joined  in  series.     If  each  lamp 
requires  0.5  amperes,  what  is  the  total  current  required  ?     What  is  the 
total  voltage  required? 

5.  If  the  three  lamps  of  problem  4  were  arranged  in  parallel,  what 
would  be  the  total  current  and  total  voltage  needed? 

6.  Six  cells,  each  having  an  e.  m.  f.  of  2  volts  and  an  internal  resist- 
ance of  0.3  ohms,  form  a  series  battery  to  send  a  current  through  a 
resistance  of  50  ohms.     How  strong  is  the  current? 

7.  If  the  cells  of  problem  6  are  arranged  in  parallel,  what  is  the  cur- 
rent strength  ? 


MEASURING  ELECTRICITY  297 

8.  Calculate  the  current  strength  sent  by  the  six  cells  of  problem  6, 
arranged  in  series,  through  an  external  resistance  of  0.1  ohms.     Also  the 
current  when  the  cells  are  in  parallel. 

9.  If  a  current  of  0.25  amperes  is  needed  in  a  telegraph  circuit,  how 
many  gravity  cells  in  series  will  be  required,  if  each  has  an  e.  m.  f .  of 
1.08  volts  and  a  resistance  of  2  ohms,  and  if  the  line  resistance  is  500 
ohms? 

10.   Six  cells  are  arranged  3  in  series  and  2  in  multiple  (Fig.  255)  to 
send  a  current  through  an  external  resistance  of  4  ohms.     If  each  cell 
has  an  e.  m.  f.  of  1.5   volts   and  a  resistance  of  0.5 
ohms,  how  intense  will  the  current  be  ? 


11.  A  galvanometer,  whose  resistance  is  299  ohms,       -r  -r 
has  a  short  stout  wire  of  1  ohm  resistance  connected     _l —  I 
across  the  terminals.     What  fraction  of  the  total  cur-       T 

rent  goes  through  the  galvanometer  ?  _l —        _J — 

12.  A  storage  battery  is  sending  current  through       "^ f 

two  wires  in  parallel,  each  having  a  resistance  of  10 

ohms.     If  the  current  through  the  battery  is  6  am-   F\0hree5i1T8erire 
peres,  what  is  the  voltage  drop  in  each  wire  ?  two  in  muitipi'e. 

13.  A  wire  of  4  ohms  is  connected  in  series  with 

2  wires  joined  in  parallel  and  having  resistances  of  8  and  12  ohms.     Find 
the  total  resistance. 

14.  A  dry  cell  when  tested  with  a  voltmeter  showed  1.5  volts,  and 
when  tested  with  an  ammeter  whose  resistance  was  negligible,  gave  7.5 
amperes.     Find  the  internal  resistance  of  the  cell. 

15.  If  the  voltage  drop  in  a  trolley  line  carrying  150  amperes  is  12.5 
volts,  what  is  the  resistance  of  the  line? 

296.  Computation  of  resistance.  For  the  measurement  of 
voltage  and  of  intensity  of  current  we  have  direct  reading 
voltmeters  and  ammeters,  but  as  yet  we  have  no  simple 
instrument  for  measuring  resistance  directly  in  ohms.  In 
many  cases,  however,  we  can  compute  the  resistance  of  a 
wire,  if  we  know  its  material,  length,  size,  and  temperature. 

Since  wires  are  usually  round,  it  is  inconvenient  to  com- 
pute their  area  of  cross  section  in  square  inches.  Conse- 
quently electrical  engineers  call  a  wire,  which  is  one 
thousandth  of  an  inch  in  diameter,  1  mil  in  diameter  and 
its  area  of  cross  section  1  circular  mil.  Inasmuch  as  the 
areas  of  circles  vary  as  the  squares  of  their  diameters,  the 


298  PRACTICAL  PHYSICS 

area  of  a  wire  expressed  in  circular  mils  is  equal  to  the  square, 
of  its  diameter  expressed  in  mils. 

For  example,  suppose  a  wire  is  0.015  inches  in  diameter.  What  is  its 
cross  section  in  circular  mils? 

0.015  inches  =  15  mils  ;  area  =  (15)2  =  225  circular  mils. 

The  resistance  of  a  wire  is  usually  computed  by  comparing 
it  with  the  resistance  of  a  wire  of  the  same  material  and  of 
a  standard  size  and  length.  The  standard  usually  chosen 
is  1  foot  long  and  1  circular  mil  in  area  of  cross  section. 
Such  a  piece  of  wire  is  called  a  mil  foot  of  wire. 

The  resistance  of  a  mil  foot  of  wire  is  sometimes  called 
the  specific  resistance  of  the  substance  of  which  the  wire  is 
made.  For  example,  the  specific  resistance  of  copper  is  about 
10.4  ohms,  of  aluminum  17.4  ohms,  and  of  iron  64  ohrns. 

Since  the  resistance  of  a  conductor  varies  directly  as  its 
length  and  inversely  as  its  area  of  cross  section,  we  can 
readily  compute  the  resistance  of  a  wire  when  its  length  and 
diameter  are  given. 

Suppose  we  wish  to  find  the  resistance  of  500  feet  of  #18  copper  wire. 
Since  the  specific  resistance  of  copper  is  10.4,  we  know  that  the  resist- 
ance of  1  mil  foot  of  copper  wire  is  10.4  ohms.  So  that  of  500  feet  of 
copper  wire  1  mil  in  diameter  is  500  x  10.4,  or  5200  ohms.  But  from  the 
wire  tables  given  on  page  304,  we  find  that  #18  wire  is  40.3  mils  in  diam- 
eter. Therefore  its  cross  section  is  (40.3)2,  or  1624  circular  mils.  There- 
fore the  resistance  will  be  j^V?  of  the  resistance  of  a  wire  1  mil  in 
diameter,  or 

X   520°  =  3'2  ohms' 


As  this  computation  has  to  be  made  very  often  in  practical  work,  it  is 
convenient  to  put  it  in  the  form  of  an  equation. 

7?      kl 

R  =  ^ 

where  R  =  resistance  in  ohms, 

k  =  specific  resistance  (ohms  per  mil  foot), 

I  =  length  in  feet, 

d  =  diameter  in  mils. 
Thus  fl  =  10102  =3.2  ohms. 


MEASURING  ELECTRICITY 


299 


297.  Effect  of  temperature  on  resistance.  If  we  coil  about  10 
feet  of  #30  iron  wire  around  a  piece  of  asbestos  and  send  a  current 
through  it, kwe  can  observe  with  a  lecture-table  ammeter  that,  as  we  heat 
the  jvire  in  a  Bunsen  flame,  the  intensity  of  the  current  is  greatly  reduced. 

If  we  connect  an  incandescent  lamp  in  series  with  a  coil  of  iron  wire, 
as  shown  in  figure  256,  we  can  observe  by  the  dimming  of  the  lamp  that 
the  current  becomes  less  when  the  iron  wire  is  heated. 

Experiments  show  that  the  resistance  of  1  mil  foot  of  copper 
wire  at  20°  C  or  68°  F  is  10.4  ohms,  while  at  0°  C  it  is  9.6 
ohms.  The  resistance  of  a  one-ohm  coil  of  copper,  correct  at 
0°  C,  increases  as  the  temperature 
rises,  approximately  0.0042  ohms 
for  each  degree.  For  example,  a 
coil  which  measures  10  ohms  at  0° 
C  will  at  50°  C  have  a  resistance 
of  10  +  (0.0042  x  50  x  10)  =  12.1 
ohms.  By  carefully  measuring 
the  resistance  of  a  wire  when  cold 
and  then  when  hot,  we  have  an  ^ 
electrical  method  of  measuring 
temperature. 

Most  pure  metals  have  nearly  the  same  rate  of  increase  of 
resistance  with  rise  of  temperature.  Most  alloys  of  metals 
not  only  have  a  much  higher  resistance  than  the  pure  metals 
of  which  they  are  made,  but  are  much  less  affected  by  tem- 
perature changes.  For  example,  "  manganin  "  is  an  alloy 
of  copper,  nickel,  and  iron  manganese,  which  has  a  specific 
resistance  of  from  250  to  450  ohms  according  to  the  propor- 
tion of  the  metals  used,  but  its  resistance  shows  scarcely  any 
change  with  temperature. 

There  are  a  few  substances,  such  as  carbon,  glass,  and 
porcelain,  which  decrease  in  resistance  when  heated.  For 
example,  the  resistance  of  a  carbon  filament  lamp  when  it  is 
hot  is  about  half  of  the  resistance  of  the  same  filament  when 
it  is  cold. 


FIG.  256.  —  Iron  wire  when  hot  has 
more  resistance  than  when  cold. 


300  PRACTICAL  PHYSICS 

PROBLEMS 

Find  the  resistance  of  each  of  the  wires  described  in  problems  1  to  6 :  — 

1.  One  mile,  #  10  copper  wire,  diameter  0.102  inches. 

2.  Fifty  feet,  #  16  copper  wire,  diameter  0.051  inches. 

3.  Twenty  feet,  #  30  copper  wive,  diameter  0.010  inches. 

4.  Two  miles,  #  14  iron  wire,  diameter  0.064  inches. 

5.  Two  hundred  feet,  #  10  iron  wire,  diameter  0.102  inches. 

6.  Five  thousand  feet,  #6  aluminum  wire,  diameter  0.162  inches. 

7.  Find  the  number  of  feet  of  #  20  iron  wire  needed  to  make  a  resist- 
ance of  5  ohms. 

8.  Find  the  diameter  of  a  copper  conductor  which  has  a  resistance 
of  2  ohms  per  1000  feet. 

9.  What  size  of  copper  wire  must  be  used  for  a  trolley  wire  4  miles 
long,  if  the  line  resistance  must  not  exceed  2  ohms? 

10.  What  is  the  "line  drop,"  that  is,  voltage  drop,  in  a  4-mile  copper 
wire  carrying  100  amperes,  if  the  wire  is  0.325  inches  in  diameter?  (Volt- 
age drop  E  =  IR.) 

298.  Rheostats  and  resistance  boxes.  To  control  an  elec- 
tric current,  we  must  regulate  either  the  voltage  or  the 
resistance.  As  electricity  is  usually  supplied  to  us  at  fixed 
voltages,  such  as  110,  220,  or  500  volts,  we  have  to  control 
the  intensity  of  the  current  by  a  variable  resistance,  called  a 
rheostat.  For  example,  in  starting  a  motor,  for  reasons  which 
will  be  discussed  in  Chapter  XVIII,  the  current  must  not  be 
thrown  on  at  full  intensity  at  first,  and  so  a  rheostat  (Fig. 
257)  is  inserted.  By  moving  a  lever  arm  the  resistance  is 
gradually  cut  out  as  the  motor  comes  up  to  speed.  Rheostats 
are  usually  made  of  some  high-resistance  alloy  such  as  German 
silver,  or  of  carbon  (lamps),  or  sometimes  of  water  with  a 
little  salt  dissolved  in  it. 

It  is  not  enough  to  know  the  resistance  of  a  rheostat.  We 
must  know  also  its  carrying  capacity,  for  the  electrical  energy 
consumed  in  the  rheostat  is  converted  into  heat  and  must  be 
radiated  off  as  fast  as  it  is  produced.  Otherwise  the  temper- 
ature will  rise  to  a  dangerous  point,  so  that  the  wire  melts  or 
sets  on  fire  things  which  are  near  it. 


MEASURING  ELECTRICITY 


301 


A  resistance  box  is  also  made  of  resistance  coils,  but  since 
they  are  used  for  electrical  measurements  which  involve  only 


FIG.  257.  — Starting  rheostat. 

small  currents,  they  have  very  small  carrying  capacity.  The 
coils  have  definite  resistances,  such  as  1,  2,  3,  5,  10,  20  ohms, 
and  are  made  of  a  wire  which  is  only  slightly  affected  by 
temperature  changes.  The  resistance  box  corresponds  for 
electrical  measurements  to  a  set  of  weights  used  in  weighing. 
For  convenience,  the  coils  are  usually  mounted  in  a  box,  as 
shown  in  figure  258,  which  has  an  insulating  hard  rubber 


FIG.  258.  —Resistance  box. 


top.  On  this  are  fastened  a  series  of  brass  blocks  which  can 
be  connected  by  brass  plugs  which  fit  between  them.  Inside 
the  box  are  the  various  coils  wound  on  spools.  The  ends  of 
a  coil  are  connected  to  adjoining  blocks,  so  that  each  gap  is 


302 


PRACTICAL  PHYSICS 


Voltmeter 


Ammeter 


bridged  inside  by  a  coil.  At  each  end  of  the  series  of  blocks 
is  a  terminal  binding  post.  When  all  the  plugs  are  firmly  in 
place,  the  only  resistance  is  that  of  the  series  of  blocks  and 

of  the  plugs  themselves,  which  is 
usually  negligible;  but  when  a  cer- 
tain plug  is  removed,  the  resistance 
of  that  coil  is  introduced. 

299.    Measurement  of  resistance 
by  voltmeter-ammeter  method.    As 
has  been  said,  there  is  no  simple 
instrument  for  measuring  a  resist- 
ance   directly,    as    the    voltmeter 
measures  voltage,  or  an  ammeter 
current.    But  there  are  two  ways  of 
measuring  a  resistance  indirectly. 
If  extreme  accuracy  is  not  required,  the  method  shown  in 
figure  259  is  commonly  used.     The  unknown  resistance  is 
placed  in  series  with  an  ammeter,  and  the  voltage  across  the 
resistance  is  obtained  by  a  voltmeter.     Then,  by  Ohm's  law, 

E 


Battery 

FIG.  259.  —  Resistance  measured 
by  a  voltmeter  and  an  am- 
meter. 


It  is  essential  that  the  resistance  of  the  voltmeter  be  so  high 
that  practically  no  current  goes  through  it.  This  method 
also  requires  that  both  ammeter  and  voltmeter  be  accurately 
calibrated  ;  that  is,  compared  with  standard  instruments  and 
the  errors  noted. 

300.  Measurement  of  resistance  by  Wheatstone  bridge.  A 
more  accurate  method  of  measuring  resistance  is  the  Wheat- 
stone  bridge,  which  is  a  machine  for  balancing  resistances.  It 
consists  essentially  of  a  loop  of  four  resistances,  R,  JT,  w, 
and  /&,  arranged  as  in  figure  260.  When  the  key  (jfiT)  is 
closed,  the  current  from  the  cell  flows  into  the  loop  at  J., 
and  there  divides  so  that  part  (Tj)  goes  through  AC  and 
part  (Jg)  through  AD.  A  sensitive  galvanometer  is  con- 


MEASURING  ELECTRICITY 


303 


nected  between  (7  and  D. 
Then  the  resistances  R, 
m,  and  n  are  so  adjusted 
that  no  current  flows 
through  the  galvanom- 
eter, which  means  that 
all  of  Jj  has  to  go  on 
through  CB  and  all  of  Iz 
through  DB,  and  also  that 
0  and  D  are  "  equipo- 
tential  "  points.  When 
this  adjustment  has  been 
made,  the  voltage  drop 
across  AC  is  J^,  and 
the  voltage  drop  across 
AD  -i§  I2m.  But  since 
C  and  D  are  at  the  same 


's 

D 
4                  || 

'l 

^1*^2 

CVH 

'    /fei; 

Cell 

FIG.  260.  —  Wheatstone  bridge  to  balance  re- 
sistances. 


potential,  these  voltage  drops  are  equal,  and 


For  similar  reasons 


(2) 


Dividing  equation  (1)  by  equation  (2),  we  have 

R_  m, 
X~  n 

From  this  fundamental  equation  of  the  Wheatstone  bridge, 
if  we  know  R,  m,  and  w,  we  can  compute  X. 

In  one  form  of  this  apparatus  the  resistance  ADB  consists 
of  a  wire  of  uniform  cross  section  one  meter  long.  Since 
the  resistances  m  and  n  are  then  directly  proportional  to  the 
distances  AD  and  DB,  the  equation  becomes 


R 
X 


Distance  AD 
Distance  DB* 


304 


PRACTICAL  PHYSICS 


WIRE  TABLES 
American  or  Brown  and  Sharp  (B.  and  S.)  Gauge 


GAUGE 

DIAMETER  IN 

MILS 

AREA  IN  CIRCULAR 
MILS 

DIAMETER  IN 
MILLIMETERS 

CARRYING  CA- 
PACITY, KUBBER 

INSULATION, 
AMPERES 

0000 

460. 

211,600. 

11.68 

210. 

000 

410. 

167,800. 

10.40 

177. 

00 

365. 

133,100. 

9.27 

150. 

0 

325. 

105,500. 

8.25 

127. 

1 

289. 

83,690. 

7.35 

107. 

2 

258. 

66,370. 

6.54 

90. 

3 

229. 

52,630. 

5.83 

76. 

4 

204. 

41,740. 

5.19 

65. 

6 

181.9 

33,100. 

4.62 

54. 

6 

162.0 

26,250. 

4.12 

46. 

7 

144.3 

20,820. 

3.67 



8 

128.5 

16,510. 

3.26 

33. 

9 

114.4 

13,090. 

2.91 

. 

10 

101.9 

10,380. 

2.59 

24. 

11 

90.7 

8,234. 

2.31 

—  '  — 

-12 

80.8 

6,530. 

2.05 

17. 

13 

72.0 

5,178. 

1.83 



-14 

64.1 

4,107. 

1.63 

12. 

15 

57.1 

3,257. 

1.45 



1<> 

50.8 

2,583. 

1.29 

6. 

17 

45.3 

2,048. 

1.15 



18 

40.3 

1,624. 

1.02 

3. 

19 

35.4 

1,288. 

.90 

20 

32.0 

1,022. 

.81 

21 

28.5 

810. 

.72 

22 

25.3 

643. 

.64 

23 

22.6 

509. 

.57 

-24 

20.1 

404. 

.61 

25 

17.90 

320. 

.46 

-26 

15.94 

254. 

.41 

27 

14.20 

202. 

-  -36 

__-28 

12.64 

159.8 

.32 

29 

11.26 

126.7 

.29 

-30 

10.02 

100.5 

.26 

31 

8.93 

79.7 

.23 

32 

7.95 

63.2 

.20 

33 

7.08 

50.1 

.18 

34 

6.30 

39.7 

.16 

35 

5.61 

31.5 

.14 

-  36 

5.00 

25.0 

.13 

37 

4.45 

19.83 

.11 

38 

3.96 

15.72 

.10 

39 

3.5§ 

12.47 

.09 

40 

3.14 

9.89 

.08 

MEASURING  ELECTRICITY  305 

where  R  is  a  known  resistance,  such  as  a  resistance  box, 
and  the  distances  AD  and  DB  are  read  off  on  a  meter  stick. 
It  may  help  one  to  remember  this  equation  to  observe  that 

Left  resistance     _  Left  distance 
Right  resistance     Right  distance 

For  example,  suppose  R  is  5  ohms  and  AD  is  45.5  centimeters;  then 
DB  is  54.5  centimeters,  and  . 

5  ^45.5 
X     54.5' 
X  =  6.05  ohms. 

PROBLEMS 

1.  Compute  the  resistance  of  a  lamp  through  which  a  voltage  of  113 
volts  sends  a  current  of  0.4  amperes. 

2.  Find  the  resistance  of  a  street-car  heater  which  takes  5  amperes 
of  current  from  a  550  volt  line. 

3.  A  wire  50  feet  long  has  a  drop  of  2  volts  across  it.     Find  the  drop 
across  20  feet. 

4.  In  a  slide-wire  Wheatstone  bridge,  the  known  resistance  is  12 
ohms,  and  the  balance  is  obtained  when  AD  (Fig.  260)  is  42.5  centi- 
meters.    Compute  the  value  of  the  unknown  resistance. 

5.  In  testing  a  Wheatstone  bridge,  4  ohm  and  6  ohm  coils  are  in- 
serted in  the  loops  AC  and  CB.     Find  the  position  which  D  should 
have  on  the  meter  wire  ADB. 


SUMMARY   OF  PRINCIPLES   IN   CHAPTER  XVI 

Unit  of  current  is  ampere.     Corresponds  to  gallons  per  second. 
Unit  of  resistance  is  ohm.     Corresponds  to  friction  in  pipe. 
Unit  of  e.  m.  f.  is  volt.     Corresponds  to  "  head." 

Ammeter  —  low  resistance  —  put  in  series  —  carries  whole  cur- 
rent. 

Voltmeter  —  high  resistance  —  put  across  circuit  —  diverts  small 
current. 

E.  M.  F.  of  cell  =  total  pump  action  in  cell. 

Terminal  voltage  =  potential  difference  between  terminals. 


306  PRACTICAL  PHYSICS 

Terminal  voltage  less  than  e.  m.  f.  by  amount  needed  to  keep 
current  moving  through  internal  resistance  of  cell. 

Ohm's  law:  — 

Current  =      e'm'f- 


resistance 

Applies  to  whole  circuit,  or  to  any  part  of  circuit. 
If  applied  to  whole  circuit,  must  take  account  of  internal  resist- 
ance of  cell,  as  well  as  of  external  resistance. 

For  resistances  in  series :  — 
Current  everywhere  the  same. 

Resistance  of  combination  is  sum  of  resistances  of  parts. 
Voltage  across  combination  is  sum  of  voltages  across  parts. 

For  resistances  in  parallel :  — 
Total  current  through  combination  is  sum  of  currents  through 

parts. 

Conductance  of  combination  is  sum  of  conductances  of  parts. 
Voltage  across  conductors  same  for  all. 

For  cells  in  series  :  — 

E.  m.  f.  is  sum  of  e.  m.  f.'s  of  parts. 
Resistance  is  sum  of  resistances  of  parts. 
Current  same  in  all  cells  as  in  external  circuit. 

For  cells  in  parallel :  — 

E.  m.  f.  is  same  as  e.  m.  f.  of  one  cell. 

Resistance  of  n  cells  in  parallel  is  -  th  the  resistance  of  any 
one  alone. 

Current  in  each  cell  is  -  th  the  current  in  external  circuit. 
n 

Resistance  of  wire  =  specific  resistance  (mil  f°°t)  X  length  (feet). 

square  of  diameter  (mils) 

In  slide-wire  Wheatstone  bridge :  — 

Left  resistance  _  left  distance 
Right  resistance  . .  right  distance 


MEASURING  ELECTRICITY  307 

QUESTIONS 

1.  Why  are  telegraph  lines  usually  made  of  iron  wire,  while  trolley 
wires  are  made  of  copper  ? 

2.  Why  should  the  circuit  of  a  dry  cell  be  kept  open  when  the  cell 
is  not  in  use? 

3.  Why  should  a  gravity  cell  be  left  on  closed  circuit  when  not 
in  use? 

4.  What  would  happen  if  an  ammeter  were  connected  across  the 
line?     (Don't  try  it !) 

5.  What  would  happen  if  a  voltmeter  were  put  in  series  in  a  line  ? 

6.  Why  is  the  moving-magnet  type  of  galvanometer  inconvenient? 

7.  What  is  the  use  of  the  shunt  in  an  ammeter? 

8.  A  copper  wire  and  an  iron  wire  of  the  same  length  are  found  to 
have  the  same  resistance.     Which  is  the  larger? 

9.  Why  do  we  get  a  more  intense  current  by  moving  the  plates  of  a 
cell  close  together? 

10.  What  is  the  effect  on  the  current  strength  of  allowing  the  liquid  to 
evaporate  to  half  its  volume  in  a  sal-ammoniac  cell,  and  why? 

11.  What  instruments  would  we  need  in  addition  to  a  coulombmeter 
to  measure  the  intensity  of  a  current? 

12.  Why  should  keys  be  inserted  in  both  the  battery  line  and  the 
galvanometer  line  of  a  Wheatstone  bridge? 

13.  Why  are  electric  bells  usually  arranged  in  parallel  instead  of  in 
series  ? 


CHAPTER   XVII 


INDUCED   CURRENTS 

Induction  by  permanent  magnets  —  direction  of  induced  cur- 
rent—  induction  by  electromagnets  —  induction  coil  —  jump 
spark  ignition  —  self-induction  —  make  and  break  ignition  — 
telephone. 

301.  Faraday's  discovery.  If  we  had  to  depend  on  bat- 
teries for  all  our  electric  currents,  we  should  not  be  lighting 
our  streets  and  houses  with  electric  lamps  or  riding  on  electric 
cars.  The  cost  of  zinc  as  a  fuel  in  the  voltaic  cell  makes  the 
battery  too  expensive  as  a  source  of  large  quantities  of 
electricity. 

It  is,  however,  possible  to  turn  mechanical  energy  directly 
into  electrical  energy  by  means  of   a  machine  called  a  dy- 
namo, in  which  currents  are  induced  by  moving  magnets.     It 
^._v=^i%?,  was  the  discovery  of  the  dynamo 

that  made  possible  the  modern 
age  of  electricity. 

302.  Currents  induced  by  mag- 
nets. If  we  connect  the  ends  of  a  coil 
of  many  turns  of  fine  insulated  wire  to 
a  lecture-table  galvanometer,  and  then 
move  the  coil  quickly  down  over  one 
pole  of  a  strong  horseshoe  magnet,  as 
shown  in  figure  261,  we  observe  a  de- 
flection. When  we  raise  the  coil  again, 
we  observe  a  deflection  in  the  opposite  direction.  If  we  lower  the  coil 
again  and  hold  it  down,  we  find  that  the  galvanometer  pointer  conies 
back  to  zero.  If  we  repeat  the  experiment,  moving  the  coil  down  slowly 
and  up  slowly,  we  find  that  the  deflection  is  less  than  before. 

308 


FIG.  261.  —  A  coil  moving  in  a  mag- 
netic field  generates  a  current. 


INDUCED   CURRENTS  309 

Such  experiments  show  that  it  is  possible  to  produce 
momentary  electric  currents  without  a  battery.  An  electric 
current  produced  by  moving  a  coil  in  a  magnetic  field  is  called 
an  induced  current.  It  is  evident  from  the  experiment  that 
the  current  is  induced  only  when  the  wire  is  moving  and  that 
the  direction  of  the  current  is  reversed  when  the  motion 
changes  direction.  Since  an  electric  current  is  always  made 
to  flow  by  an  electromotive  force,  the  motion  of  a  coil  in  a 
magnetic  field  must  generate  an  induced  electromotive  force. 
Experiments  have  shown  that  this  induced  electromotive 
force  varies  directly  as  the  speed  of  the  moving  coil. 

303.  Direction  of  induced  currents.    If  we  take  the  same  apparatus 
(Fig.  261)  and  move  the  coil  down  over  the  ./V-pole  of  the  magnet  and 
then  down  over  the  S-pole,  we  find  that  the  deflections  are  in  opposite 
directions  in  the  two  cases.     To  determine  in  which  direction  the  induced 
current  is  flowing  in  the  coil,  one  may  make  a  little  voltaic  cell  by  putting 
in  his  rnouth  a  copper  wire  and  a  zinc  wire  connected  to  the  galvanometer. 
Since  we  know  that  the  copper  is  the  positive  electrode,  we  can  compare 
the  direction  of  the  galvanometer  deflection  caused  by  the  cell  current 
with  that  caused  by  the  induced  current,  and  so  determine  the  direction 
of  the  latter.     In  this  way  we  find  that  when  the  coil  is  moving  down 
over  the  ^V-pole  of  the  magnet,  the  induced  current  is  in  such  a  direction 
that  the  lower  face  of  the  coil  is  an  ^-pole.     In  a  similar  way  we  find 
that  when  the  coil  is  brought  down  over  the  £-pole  of  the  magnet,  the 
induced  current  is  in  such  a  direction  that  the  lower  face  of  the  coil  is  an 
<S-pole.     In  both  cases  the  lower  face  of  the  coil  is  a  pole  of  such  a  sort 
as  to  be  repelled  by  the  pole  toward  which  it  is  moving. 

The  direction  of  induced  currents  may  be  stated  as 
follows :  An  induced  current  has  such  a  direction  that  its 
magnetic  action  tends  to  resist  the  motion  by  which  it  is  pro- 
duced. 

304.  Currents  induced  by  currents.    Since  an  electromagnet 
can  be  made  more  powerful  than  a  steel  magnet,  we  would 
expect  greater  induced  currents  when  we  move  an  electro- 
magnet near  a  coil. 

We  will  connect  the  secondary  coil  S  in  figure  262  to  a  galvanometer 
and  the  primary  coil  P  to  a  battery.  When  we  move  the  current-carry- 


310  PRACTICAL   PHYSICS 

ing  primary  coil  P  either  into  or  out  of  the  other  coil  S,  a  current  is  in. 

duced,  just  as  when  we  move  a  magnet  in  and  out  of  a  coil.     The  induced 

current  is,  however,  much  greater.  We 
find  also  that  a  stronger  current  in  the 
coil  P  increases  the  strength  of  the 
magnetic  field,  and  so  of  the  induced 
current. 

We  may  also  increase  the  induced 
currents  by  inserting  an  iron  core  in- 
side the  primary  coil.  This  greatly 
strengthens  the  magnetic  field  and  so 
increases  the  number  of  lines  of  force 
about  the  coil. 

FIG.  262. -A moving electr^agnet         If  we  Pufc  the  Primary  coil  with  its 

generates  a  current.  iron  core  inside  the  secondary  coil,  we 

can   generate  an   induced  current  by 

opening  and  closing  a  switch  in  the  primary  circuit.    When  the  switch  is 

opened  and  closed,  the  deflections  are  in  opposite  directions. 

Ill  general  we  see  that  an  induced  current  is  set  up  in  a 
coil  whenever  there  is  a  change  in  the  number  of  lines  of  mag- 
netic force  passing  through  the  coil. 

QUESTIONS 

1.  Show  how  a  current  can  be  produced  in  a  coil  of  wire  by  the  motion 
of  a  magnet. 

2.  Why  is  it  necessary  in  the  experiment  just  described  to  use  a  coil 
of  many  turns  ? 

3.  Show  how  a  coil  of  wire  should  be  rotated  in  the  earth's  magnetic 
field  to  get  the  maximum  induced  current. 

4.  Show  how  a  coil  of  wire  can  be  rotated  in  the  earth's  magnetic 
field  so  as  to  get  no  induced  current. 

305.  Induction  coil.  In  the  induction  coil  (Fig.  263)  the 
core  c  is  made  of  soft  iron  wires;  the  primary  coil  P  consists 
of  a  few  turns  of  large  copper  wire,  and  the  secondary  coil  s, 
which  is  carefully  insulated  from  the  primary,  contains  many 
turns  of  very  small  silk-covered  copper  wire.  To  make  and 
break  the  primary  current  very  rapidly,  an  interrupter  H  is 
commonly  made  to  operate  on  the  end  of  the  coil.  This 


INDUCED   CURRENTS 


311 


automatic  make  and  break  works  exactly  like  the  electric 
bell  described  in  section  269.  When  the  primary  circuit  in 
such  a  coil  is  broken,  the  current  tends  to  keep  on  as  if  it 
had  inertia,  and  may  jump  the  switch  gap  at  A  even  after  it 
has  opened  slightly.  This  slows  up  the  "  break  "  and  weakens 


FIG.  263.  —  Induction  coil. 

the  induced  e.m.f.  So  a  condenser  J  is  connected  across 
the  gap.  It  is  usually  made  of  sheets  of  tin  foil,  insulated 
by  paraffin  paper,  arranged  as  shown  in  figure  263.  This 
furnishes  a  storage  place  into  which  the  current  can  surge 
when  broken,  and  diminishes  the  sparking  at  the  interrupter. 
Even  with  a  condenser  there  is  some  sparking,  and  so  the 
contact  points  have  to  be  tipped  with  silver  or  platinum  and 
frequently  cleaned. 

Coils  are  generally  rated  according  to  the  distance  between 
the  terminals  of  the  secondary  across  which  a  spark  will 
jump.  When  the  coil  is  in  operation,  sparks  jump  across 
this  gap  in  rapid  succession,  provided  the  terminals  are  close 
enough  together.  This  type  of  coil  is  sometimes  called  the 
Ruhmkorff  coil  and  is  the  one  in  general  use  for  jump-spark 
ignition  on  gas  engines. 

306.  Uses  of  induction  coils.  Jump-spark  ignition  is  the 
most  important  practical  application  of  the  induction 
coil.  Small  induction  coils  are  also  used  under  the  name  of 
medical  or  household  coils.  These  are  usually  so  made  that  the 
strength  of  the  induced  current  in  the  secondary  can  be 


312 


PRACTICAL  PHYSICS 


varied  either  by  moving  the  primary  coil  in  and  out  of  the 
secondary,  or  by  moving  in  and  out  a  brass  tube  which  fits 
around  the  core.  In  recent  years  very  large  and  powerful 
induction  coils  have  been  built  for  exciting  X-ray  tubes  and  for 
setting  up  electric  waves  for  wireless  telegraphy.  These  uses 
will  be  described  in  Chapter  XXIV. 

307.  Self-induction.  It  is  a  familiar  fact  in  mechanics  that 
bodies  act  as  if  disinclined  to  change  their  state,  whether  of 
rest  or  motion,  and  we  call  this  tendency  inertia.  We  have 
found  a  similar  electrical  phenomenon,  when  the  primary  of 
an  induction  coil  is  broken.  Let  us  examine  it  more  closely. 
If  an  electric  circuit  contains  a  coil  of  wire  with  many 
turns  and  with  a  soft  iron  core,  it  opposes  the  building  up  of 
a  current  at  the  start,  and  when  the 
circuit  is  broken,  the  current,  once 
started,  tries  to  keep  on  flowing,  as 
shown  by  the  spark  at  the  gap.  This 
electromagnetic  inertia  of  a  circuit  is 
called  its  self-induction. 


To  show  self-induction,  we  may  put  a  small 
lamp  across  the  terminals  of  a  large  electro- 
magnet.     If  we   throw  on   some  supply  of 
direct  current,  as  from  a  storage  battery,  as 
shown  in  figure  264,  the  lamp  lights  up  at 
first,  but  quickly  dies  down  when  the  current 
FIG.  264.  —  Self-induction  of    becomes  steady.    When  the  switch  is  opened, 
an  electromagnet.  the  lamp  again  lights  up. 

In  this  experiment,  when  the  circuit  is  closed,  the  self- 
induction  of  the  coil  opposes  the  flow  of  current  through  the 
electromagnet,  and  so  the  current  has  to  go  through  the  lamp. 
When  the  circuit  is  opened,  self-induction  causes  the  current 
to  continue  to  flow,  and  the  lamp  is  its  only  available  path. 
Self-induction,  then,  occurs  only  when  the  current  is  changing. 

308.  Applications  of  self-induction.  The  principle  of  self- 
induction  is  made  use  of  in  make-and-break  ignition.  A  single 


INDUCED   CURRENTS 


313 


FIG.  265.  —  Make-and-break  spark 
coil. 


coil  is  used,  consisting  of  many  turns  of  wire  wound  on  a 

soft  iron  core.      When  such  a  coil  is  employed  to  furnish  a 

spark   in  the  cylinder  of  a  gas 

engine,  the  circuit  is  as  shown 

in   figure   265.       The    terminals 

are  two  points  inside  the  cylin- 
der of  the  engine,  one  stationary 

(yl)  and  the  other  moving  (J5). 

When    A   and   B   separate,    the 

self-induction  of  the  coil  causes 

enough  induced  e.m.f.  to  make 

a    spark    jump   across    the   gap 

between  them. 

This  is  the  kind  of  coil  which  is  used  to  light  gas  Jjurners 

in  houses  by  means  of  a  battery  current.     If  the  circuit  of  a 

large  electromagnet,  such  as  the  field  of  a  dynamo,  is  broken, 

while  one  is  touching  the  conductors  on  either  side  of  the 

gap,  the   current  due  to  self-induction   sometimes   gives   a 

severe  shock. 

309.  Telephone  receiver.  In  1876 
Alexander  Graham  Bell  astonished 
the  world  by  showing  that  the 
sound  of  the  human  voice  could  be 
transmitted  by  electricity.  The 
essential  part  of  his  apparatus  was 
what  we  still  use  and  know  as  the 
Bell  receiver.  The  hard  rubber  case 
contains  a  steel  U~snaPe(i  magnet, 
which  has  around  each  pole  a  coil 
of  many  turns  of  very  fine  wire 
(Fig.  266).  A  disk  of  thin  sheet 
iron  is  so  supported  that  its  center 
does  not  quite  touch  the  ends  of 

the  magnet.     A  hard  rubber  cap  or  earpiece  with  a  hole  in 

the  center  holds  the  disk  in  place. 


w 


FIG.  266.  —  Bell  telephone  re- 
ceiver. 


314 


PRACTICAL    PHYSICS 


To  show  the  operation  of  the  telephone  receiver,  we  will  connect  a 
receiver,  in  series  with  a  lamp,  to  the  A.C.  mains  or  to  a  magneto, 
which  furnishes  an  alternating  current.  We  immediately  hear  a  loud 
hum.  If  we  hold  the  receiver  upright  and  stand  a  pencil  on  the  dia- 
phragm, it  dances  up  and  down.  The  alternating  current,  sent  through 
the  coil,  alternately  opposes  and  strengthens  the  magnet,  which  attracts 
the  disk  alternately  more  and  then  less,  thus  causing  it  to  vibrate.  This 
sets  the  air  to  vibrating  and  produces  sound. 

310.  The  microphone.     To  understand  how  the  right  sort 
of  currents  can  be  produced  to  make  a  telephone  receiver 

speak  words  instead  of 
merely  humming,  we  will 
set  up  an  old  fashioned 
instrument  called  a  mi- 
crophone. 

A  simple  microphone  can  be 
FIG.  267.-Carbon  microphone.  made  Qut  of  three  lead  ^^ 

or  three  pieces  of  electric  light  carbon,  or  out  of  a  single  carbon  resting 
across  two  old  safety  razor  blades  (Fig.  267).  If  such  a  microphone  is 
connected  in  series  with  a  battery  and  telephone  receiver,  and  a  watch  is 
laid  on  its  baseboard,  the  ticks  can  be  heard  in  the  telephone  even  if  it 
is  some  distance  away.  The  little  jars  which  the  watch  gives  the  base- 
board shake  the  carbons  so  that  the  resistance  at  their  points  of  contact 
varies  and  thus  changes  the  current.  The  changing  current  then  pulls 
the  telephone  diaphragm  back  and  forth,  and  sets  the  surrounding  air  in 
motion. 

311.  The  telephone  transmitter.     The  ;nodern  "  solid  back  " 
telephone  transmitter  is  simply  a  carefully  designed  microphone. 
It  contains  a  little  box  O  (Fig.  268) 

which  is  filled  with  granules  of  hard  car- 
bon. The  front  and  the  back  of  the  box 
are  polished  plates  of  carbon,  and  the 
sides  of  the  box  are  insulators.  The 
front  carbon  is  attached  to  the  center 
of  the  diaphragm  2),  and  moves  in  and 
out  a  little  when  the  diaphragm  vi- 

,  '         .      7?  >      ***•  208.—  Carbou  trans- 

brates.      The   other  plate   is  fastened  mitter. 


INDUCED   CURRENTS 


315 


rigidly  to  the  solid  back  of  the  case.  A  current  from  a  battery 
flows  through  the  diaphragm  to  the  front  plate,  then  back 
through  the  granules  to  the  other  plate,  and  then  out  along 
the  telephone  line  to  a  receiver.  When  the  diaphragm  moves 
back  a  little,  it  compresses  the  granules,  their  resistance  de- 
creases, and  the  current  gets  stronger  and  pulls  the  diaphragm 
of  the  receiver  back  also.  When  the  transmitter  diaphragm 
moves  out,  the  current  decreases  and  the  receiver  diaphragm 
moves  out  also.  So  all  the  motions  of  the  transmitter 
diaphragm  are  reproduced  l>y  the  receiver  diaphragm.  If 
one  speaks  into  the  transmitter,  causing  its  diaphragm  to 
move  in  a  corresponding  way,  the  receiver  diaphragm  moves 
in  the  same  way  and  produces  the  same  kind  of  waves  in  the 
surrounding  air. 

312.  Central  vs.  local  batteries.  The  system  we  have  just 
described  is  the  one  in  use  in  all  large  cities.  The  battery 
is  a  large  storage  battery  (or  a  dynamo)  at  the  central  sta- 
tion and  is  used  on  all  the  lines  that  happen  to  be  busy  at 
any  instant. 

In  many  country  exchanges  and  on  isolated  lines  another 
system,  called  the  local 
battery  system,  is  used 
because  it  is  cheaper  to 
install  and  maintain. 
Even  in  cities  some- 
thing equivalent  to  this 
system  is  used  in  "long- 
distance "  work. 

In  this  system  (Fig.  269)  each  subscriber's  telephone  set 
contains  a  few  dry  cells  which  are  connected  in  series  with 
his  transmitter,  as  already  described.  But  the  varying  cur- 
rent produced,  instead  of  being  sent  directly  out  on  to  the 
line,  goes  to  the  primary  of  a  little  induction  coil  and  back 
to  the  battery.  The  secondary  of  the  induction  coil  mean- 
while sends  out  into  the  line  an  induced  current  that  varies 


ine 


Transmitter   .. 

Receiver 

FIG.  269.  —  Local  battery  telephone  system. 


316  PRACTICAL  PHYSICS 

exactly  like  the  primary  current,  but  is  at  much  higher  volt- 
age. This,  as  we  shall  see  in  Chapter  XVIII,  makes  the 
"  line  losses  "  much  smaller,  and  so  more  energy  gets  through 
to  the  receiver  than  if  the  original  current  had  been  trans- 
mitted directly. 

This  system  is  really  better,  electrically,  than  the  central 

battery  system 
(Fig.  270).  It  is 
not  used  in  large 

//„,  L-5=  cities,    chiefly    be- 

cause of  the  trouble 

Fia.  270.  —Telephone  with  central  battery. 

involved   in  keep- 
ing so  many  local  batteries  in  proper  working  condition. 

313.  Return  wire  necessary.  Telephone  circuits  used  to 
be  made  like  telegraph  circuits,  with  only  one  wire,  the 
return  being  through  the  earth.  But  in  cities  this  is  imprac- 
tical because  of  the  noise  and  confusion  caused  by  stray  cur- 
rents in  the  earth  due  to  trolley  cars  and  other  electrical 
disturbances.  So  in  cities  two  wires  are  used,  and  they  are 
put  close  together  so  that  no  currents  can  be  induced  in  them 
by  stray  magnetic  fields  from  other  circuits  (which  would 
cause  "  cross-talk  "),  or  from  lighting  and  power  circuits. 


SUMMARY  OF  PRINCIPLES  IN  CHAPTER  XVII 

Induced  current  exists  only  when  the  number  of  lines  of  force 
through  the  circuit  is  changing. 

Induced  current  has  such  a  direction  as  to  oppose  the  motion  that 
causes  it. 

Self-induction  appears  only  when  the  current  is  changing. 

The  effect  of  self-induction  is  always  to  oppose  the  change  of  the 
current. 


INDUCED  CURRENTS  317 


QUESTIONS 

1.  Why  is  it  that  the  self-induction  of  a  circuit  is  not  apparent  as 
long  as  the  current  is  steady  ? 

2.  Why  is  the  lamp  described  in  the  experiment  in  section  307  not 
bright  all  the  time  that  the  switch  is  closed? 

3.  Why  is  it  dangerous  to  touch  the  terminals  of  the  secondary  of  a 
large  Ruhmkorff  coil  ? 

4.  What  is  likely  to  happen  to  an  induction  coil  if  you  short-circuit 
the  secondary  while  the  coil  is  running? 

5.  Why  is  the  induced  e.  m.  f.  in  the  secondary  of  an  induction  coil 
so  much  greater  at  the  break  of  the  primary  than  at  the  make? 

6.  What  furnishes  the  energy  of  an  induced  current? 

7.  Upon  what  three  factors  does  the  e.  m.  f.  of  an  induced  current 
depend? 

8.  In  a  central   battery  telephone   system,  what  arrangements  are 
made  to  keep  the  battery  from  sending  current  all  the  time  through  tele- 
phone lines  not  in  use  ? 


CHAPTER   XVIII 

ELECTRIC   POWER 

The  generator — wire  cutting  lines  of  force  —  dynamo  rule 
for  direction  of  current  —  law  of  induced  e.  m.  f.  —  revolving 
loop  commutator  —  Gramme  ring  —  drum  armature  —  field  ex- 
citation. 

Electric  power  —  how  measured —  the  joule  and  watt  —  com- 
mercial units. 

Electric  heating — common  applications  —  fuses  —  computa- 
tion. 

Electric  lighting  —  the  arc  —  modern  forms  —  incandescent 
lamps  —  metal  filaments  —  efficiency. 

The  motor — side  push  on  wire  carrying  current  —  motor  rule 
for  direction  of  motion  — forms  of  motor  —  back  e.  m.  f.  —  start- 
ing box— applications  — efficiency. 

Chemical  effects  —  electrolysis  —  bleaching  —  electroplating 
. — %electrotypiug  —  refining  metals  —  electrochemical  equiva- 
lents —  storage  battery. 

THE  GENERATOR 

314.  The  importance  of  the  generator.  ^  The  most  useful 
application  of  induced  currents  did  not  come  until  nearly 
forty  years  after  Henry  and  Faraday  made  their  wonderful 
discovery.  Then  the  generator  was  developed,  by  means  of 
which  the  enormous  energy  of  steam  engines  and  water 
wheels  can  be  transformed  into  electricity.  The  electricity 
generated  in  this  way  can  be  transmitted  many  miles,  and 
used  in  motors  to  turn  all  sorts  of  machinery,  in  lamps  of 
various  kinds  to  light  our  streets  and  homes,  in  heaters  to 
warm  cars  and  sometimes  houses,  to  toast  bread  and  heat 
flatirons,  and  in  furnaces  to  melt  steel  in  iron  mills.  Thus 

318 


ELECTRIC  POWER 


519 


the  generator  has  revolutionized  modern  industry  by  furnish- 
ing cheap  electricity. 

315.  Wire  cutting  lines  of  magnetic  force.     A  simple  way 
-to  get  at  the  fundamental  idea  of  the  generator  is  to  think,  as 

Faraday  did,  of  the  induced 
e.  m.  f.  produced  in  a  single 
wire  when  it  is  moved  through 
a  magnetic  field.  Suppose 
the  straight  wire  AB  is  pushed 
down  across  the  magnetic 
field  shown  in  figure  271. 
An  induced  e.  m.  f.  is  set  up 
in  AB,  which  makes  B  of 
higher  potential  than  A,  as  FIG.  271.  -  induced  e.  m  f.  iu  a  wire 

5  r  .  cutting  lines  of  force. 

can  be  shown  by  connecting 

B  and  A  with  a  galvanometer.  As  long  as  the  wire  remains 
stationary  no  current  flows.  Even  if  the  wire  does  move, 
if  it  moves  in  a  direction  parallel  to  the  lines  of  force,  no 
current  flows.  In  short,  a  wire,  to  have  an  e.  m.  f.  induced 
in  it,  must  move  so  as  to  cut  lines  of  force. 

316.  Direction  of  induced  e.  m.  f.     We  have  just  seen  that 
when  the  wire  AB  in  figure  271  is  moved  down,  the  induced 
current  in  it  is  from  A  to  B.     If  the  wire  were  moved  up,  the 

induced  current  would  be  from  B  to 
A.  Furthermore,  if  the  field  is  re- 
versed without  changing  the  direction 
of  motion  of  the  wire,  the  current  re- 
verses. It  will  be  seen,  then,  that 
the  direction  of  the  induced  e.  m.  f. 
depends  upon  two  factors,  (#)  the  di- 
rection of  the  motion  of  the  wire  and 
(j)  tne  direction  of  the  flux  or  mag- 

!•      i»  c    <•  m  i    ,-  t 

netic  lines  ot  torce.  I  he  relation  ot 
these  three  directions  may  be  kept  in  mind  by  Fleming's 
rule  of  three  fingers,  as  shown  in  figure  272. 


FIG  272.-Right-hand  rule 

for  induced  e.  m.  f. 


320 


PRACTICAL  PHYSICS 


FLEMING'S  RULE.  Extend  the  thumb,  forefinger,  and  center 
finger  of  the  right  hand  so  as  to  form  right  angles  with  each 
other.  If  the  thumb  points  in  the  direction  of  the  motion  of  the 
wire,  and  the  forefinger  in  the  direction  of  the  magnetic  flux,  the 
center  finger  will  point  in  the  direction  of  the  induced  current. 

To  remember  this  rule,  notice  the  corresponding  initial 
letters  in  the  words  "fore"  and  "flux,"  "  center"  and  "cur- 
rent." 

317.  Amount  of  induced  C.  m.  f.  If  we  have  a  large  electromagnet 
with  flat-faced  pole  pieces  (Fig.  273),  we  can  demonstrate  the  various 

laws  about  induced  currents 
in  a  conductor.  If  we  move 
a  wire  down  through  the  gap 
between  the  pole  pieces,  a  mil- 
livoltmeter  will  show  the  in- 
duced current.  If  we  hold  the 
wire  at  rest  in  the  gap,  we  ob- 
serve no  current.  If  we  move 
the  wire  horizontally  parallel 

FIG.  273.— Electromagnet  for  demonstrating    to  the  lines  of  magnetic  flux, 
induced  e.  m.  f.  we  get  no  current.    If  we  move 

the  wire  up.  through  the  gap, 

we  observe  a  current  in  the  opposite  direction,  as  predicted  by  Fleming's 
rule.  If  we  increase  the  magnetic  field  by  increasing  the  current  through 
the  electromagnet,  we  increase  the  induced  current.  If  we  move  the  wire 
more  quickly  through  the  gap,  we  increase  the  induced  current.  Finally, 
if  we  bend  the  wire  into  a  loop  of  several  turns,  and  move  the  loop  down 
over  one  pole  so  that  all  the  wires  on  one  side  of  the  loop  pass  through 
the  gap,  we  find  that  the  current  is  increased. 

In  this  experiment  we  see  that  the  induced  e.  m.  f.  is  in- 
creased by  moving  the  wire  faster  across  the  magnetic  field, 
by  making  the  magnetic  field  stronger,  and  by  using  more 
turns  of  wire.  In  short,  the  amount  of  induced  e.  m.f.  de- 
pends on  three  factors  :  (1)  the  speed  ;  (2)  the  magnetic  field  'f 
and  (3)  the  number  of  turns. 

Experiments  show  that 

Induced  e.  m.  f .  varies  as  speed  x  flux  x  turns. 


ELECTRIC  POWER  321 

318.  Commercial  generators.      A  machine  for  converting 
mechanical  energy  into  electrical  energy  is  called  a  dynamo 
or  generator.     Its  essential  parts  are  two,  (1)  the  magnetic  field, 
which  is  produced  by  permanent  magnets,  as  in  the  magneto, 
or   by  electromagnets,  as   in   larger   generators,  and  (2) 'a 
moving  coil  of  copper  wire,  called  the  armature,  wound  on  a 
revolving  iron  ring  or  drum.      The  armature  wires  corre- 
spond to  the  moving  wires  in  the  experiments  above. 

319.  Current  in  a  revolving  loop  of  wire.     If  we  rotate  a  rectan- 
gular coil  between  the  poles  of  a  large  horseshoe  magnet,  or  better,  of  an 
electromagnet,  we  can  detect  an  electric  current  in  the  revolving  coil  by 
connecting  it  with  flexible  leads  to  a  galvanometer.     As  we  turn  the 
coil,  the  current  is  reversed  every  half  revolution. 

It  will  help  us  to  understand  just  what  is  happening  in  the 
revolving  coil  if  we 
first  consider  what 
would  happen  in  a 
single  loop  of  wire 
which  is  rotated  in 
a  magnetic  field,  as 
shown  in  figure  274. 
If  we  start  with  the 
plane  of  the  loop  ver-  Fl0'  m-  ~Sinele  "Sjjjf  turning  in  a  mag' 
tical  and  turn  the 

handle  in  a  clockwise  direction,  the  wire  BO  moves  down 
during  the  first  half  turn,  and  so,  by  Fleming's  rule,  we 
should  expect  the  induced  e.  m.  f.  to  tend  to  send  the 
current  from  0  to  B.  At  the  same  time  the  wire  AD  is 
moving  up,  and  the  current  will  tend  to  flow  from  A  to  D. 
The  result  is  that  during  the  first  half  turn  the  current 
goes  around  the  loop  in  the  direction  AD  OB.  During 
the  second  half  turn  the  current  is  reversed  and  goes  around 
in  the  direction  ABOD. 

To  show  that  this  really  does  happen  in  the  loop,  we  can 
cut  the  wire  and  connect  the  ends  to  slip  rings  x  and  y,  as 

Y 


322 


PRACTICAL  PHYSICS 


shown  in  figure  275.     The  brushes  B'  and  B",  which  rest 
on   the  rings,   are  connected   to  a  galvanometer.      In  this 

way  it  can  be  shown  that  there 
is  generated  in  the  coil  an 
alternating  current  which  reverses 
its  direction  twice  in  every  rev- 
olution. Moreover,  it  is  pos- 
sible to  show  that  the  induced 

FIG.  275.- Single  loop  connected  to     e.m.f.    starting   at    Z61'O    ffOCS   UD 
slip  rings. 

to  a  maximum  and   then   back 

to  zero  in  the  first  half  turn;  then  it  reverses  and  goes  to  a 
maximum  in  the  opposite  direction  and  finally  back  to  zero. 
The  induced  e.  m.  f .  reaches  its  maximum  when  the  coil  is 
horizontal,  because  in  this  position  the  wires  AD  and  BO 
are  cutting  lines  of 
force  most  rapidly. 
This  is  illustrated 
by  the  curve 
shown  in  figure  J-10 
276. 

Machines  which 
are  built  to  deliver 
alternating  cur- 
rents are  called  alternators  or  A.  C.  generators. 

320.    Commutator.     To  get  a  direct  current,  that  is,  one  which 
flows    always   in    the   same    direction,    we    have    to    use   a 

commutator.  To  under- 
stand how  this  works,  let 
us  study  a  very  simple 
case.  If  the  ends  of  the 
loop  in  section  319  are 
connected  to  a  split  ring, 
as  shown  in  figure  277, 

B  7  *«    -  we   may   set   the   brushes 

FIG.  277.  — Split-ring  commutator.  -B+    an(l  •B~—   on    opposite 


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' 

\ 

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, 

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FIG.  276.  —  Curve  to  show  relation  of  induced  e.m.  f. 
to  position  of  loop. 


ELECTRIC  POWER 


323 


sides  of  the  ring,  so  that  each  brush  will  connect  first  with  one 
end  of  the  loop  and  then  with  the  other.  By  properly  adjust- 
ing the  brushes,  so  that  they  shift  sections  on  the  commutator 
just  when  the  current  reverses  in  the  loop,  that  is,  when  the 
loop  is  in  a  vertical  position,  we  may  get  the  current  to 
flow  only  out  at  one  brush  B  +  ,  and  only  in  at  the 
other  brush  B— .  The  direction  of  the  current  in  the  ex- 
ternal circuit  is  always  the  same,  even  though  the  current 
in  the  loop  itself 
reverses  twice  in 
every  revolution. 

The  current  de- 
livered by  such  a 
machine  can  be 
represented  by  the 
curve  in  figure 


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POSITION  OF  LOOP    IN  DEGREES 

FIG.  278.  —  Pulsating  e.  ra.  f.  delivered  by  loop  fitted 
with  commutator. 


278.      Although  it 

is  always  in  the  same  direction,  it  is  pulsating. 

A  machine  with  a  commutator  for  delivering  direct  current 
is  called  a  direct-current  dynamo  or  D.C.  generator. 

321.  Generators  of  steady  currents.  The  e.m.f.  produced 
by  rotating  a  single  loop  in  a  magnetic  field  can  be  raised 
by  using  many  turns  of  wire  and  by  rotating  the  coil  very 
fast.  Nevertheless  the  current  will  be  pulsating,  and  this 
is  unsatisfactory  for  many  purposes.  To  get  a  machine 
to  deliver  a  steady  current,  a  Frenchman,  named  Gramme, 
invented  in  1870  the  so-called  Gramme  ring  form  of  arma- 
ture. 

The  Gramme  ring  armature  is  now  very  seldom  used,  but 
it  is  worth  studying  carefully  because  the  fundamental  prin- 
ciples of  its  action  can  be  understood  from  very  simple  dia- 
grams, whereas  most  armatures  of  the  common  or  drum  type, 
although  based  on  exactly  the  same  principles,  cannot  be 
represented 'by  simple  diagrams. 

A  rotating  soft-iron  ring  or  hollow  cylinder  is  mounted  be- 


324 


PRACTICAL  PHYSICS 


FIG.  279.  —  Magnetic  field  in  a  Gramme  ring. 


tween  the  poles  of  an  electromagnet,  as  in  figure  279.     The 

ring  serves  to  carry  the  flux  across  from  one  pole  to  the 

other.  There  are 
scarcely  any  lines  of 
force  in  the  space  in- 
side the  ring.  A  con- 
tinuous coil  of  insu- 
lated copper  wire  is 
wound  on  the  ring, 
threading  through  the 
hole  every  turn.  When 

the  ring  rotates,  as  in  figure  280,  the  wires  on  the  outside  are 

cutting  lines  of  force,  but  those  inside  are  not.     Furthermore, 

according    to    the    right- 

hand   rule,  the  outside 

wires    on    the    right-hand 

side   are   moving   in    such 

a  direction   that  the  in- 

duced current  tends  to 

flow  towards  us.      The 

wires   lying  on   the  other 

side  of  the  ring  are  mov- 

ing so  as  to  induce  a  cur- 


FIG. 280.  —  Gramme  ring  rotating  in  a  mag- 
netic field. 


rent    away    from    us.       If 
there  were  no  outside  connections,  these  two  opposing  e.  m.  f.'s 

would  just  balance,  and 
would 


no  current  would  flow. 
This  would  be  like  ar- 
ranging a  lot  of  cells  in 
series  with  an  equal 
number  turned  so  that 
they  are  opposed  to  the 
first  group  [Fig.  281 
(a)]  ;  obviously  no  cur- 
rent would  flow. 


FIG. 


281.  — Batteries  (a)  without,  and  (6)  with 
an  external  circuit. 


ELECTRIC  POWER 


325 


But  if  we  imagine  the  copper  wires  on  the  outer  surface 
of  the  ring  to  be  scraped  bare,  and  if  two  metal  or  carbon 
blocks  or  brushes  at  the  top  and  bottom  rub  on  the  wires  as 
they  pass,  a  current  could  be  led  out  of  the  armature  at  one 
brush,  and,  after  passing  through  an  external  resistance,  such 
as  a  lamp,  could  be  led  back  to  the  armature  again  at  the 
other  brush.  In  this  case  the  armature  circuit  is  double,  con- 
sisting of  its  two  halves  in  parallel.  It  is  like  adding  an 
external  circuit  to  the  arrangement  of  cells  described  above. 
This  battery  analogue  for  a  Gramme  ring  armature  is  shown 
in  figure  281  (6). 

In  the  Gramme  ring 
arrangement  there  are 
at  every  instant  the  same 
number  of  active  con- 
ductors in  each  half  of 
the  armature  circuit,  and 
so  the  current  delivered 
by  the  armature  is  not 


FIG.  282.  —  Ring  armature  with  commutator. 


only   direct    but    also 

steady. 

In  practice,  however,  it  would  be  difficult  to  make  a  good 

contact  directly  with  the  wires  of  the  armature,  because  the 

wires  must  be  carefully  insulated  from  each  other  and  from 
the  iron  core,  and  so  the  various  turns 
of  wire,  or  groups  of  turns,  have  branch 
wires  which  lead  off  to  the  commutator 
segments,  as  in  figure  282. 

The  commutator  consists  of  copper 
bars  or  segments  which  are  arranged 
around  the  shaft  and  insulated  from 
each  other  by  thin  plates  of  mica  (Fig. 
283).  To  get  a  satisfactorily  steady 

FIG.  283. -Commutator    current  there  ^ould  be  many  segments 
and  brush.  in  a  commutator,  so  that   the   brushes 


326 


PRACTICAL   PHYSICS 


FIG.  284.  —  Slotted  armature  core,  drum  type. 


may  always  be  connected  to  the  armature  circuit  in  the  most 
favorable  way. 

322.  Drum  armature.     Since  very  little  flux  passes  across 
the  air  space  in  the  center  of  a  Gramme-ring  armature,  the 

wires  on  the  in- 
ner surface  of 
the  ring  do  not 
cut  lines  of  mag- 
netic force  and 
are  useless,  ex- 
cept to  connect 
the  adjoining 
wires  on  the  outer  surface.  Furthermore,  it  is  very  incon- 
venient to  wind  the  wire  on  an  armature  of  the  ring  form. 
For  these  reasons,  most  armatures  are  now  of  the  drum  type. 
In  this  form,  the  core  is  made  with  slots  along  the  circum- 
ference for  the  wires  to  lie  in  (Fig.  284).  Since  the  active 
wires  in  one  slot  are  connected  across  the  end  to  active  wires 
in  another  slot,  there  are  no  idle  wires  inside  the  core. 

323.  Multipolar   generators.     The    machines   which   hav-e 
been  described  are  called  bipolar  machines.     For  commercial 
purposes,  especially   in   large   ma- 
chines, it  is  common  practice  to  use 

four,  six,  eight,  or  even  more  poles. 
Such  machines  are  called  multipolar. 
By  increasing  the  number  of  poles 
we  can  get  the  commercial  voltages 
(110,  220,  or  500  volts),  at  much 
slower  speeds  than  would  be  neces- 
sary in  a  bipolar  machine.  We 
have  already  seen  that  the  voltage 
depends  on  the  rate  at  which  the 

Wires  Of   the  armature  CUt   the  lines     ?IG.  285.- Four-pole  generator. 

of  magnetic  force.     Bat  in  a  four-pole  machine  (Fig.  285) 
each  wire  on  the  armature  cuts  a  complete  set  of  lines  of 


ELECTRIC  POWER 


327 


force  four  times  in  each  revolution  instead  of  twice  as  in 
a  two-pole  machine.  For  this  reason  the  speed  of  a  four- 
pole  machine  is  one  half  the  speed  required  in  a  two-pole 
machine  for  the  same  voltage.  Furthermore,  the  multipolar 
machine  is  more  economical  to  build  because  it  requires 
less  iron  to  carry  the  magnetic  flux.  It  will  be  observed 
from  the  diagram  (Fig.  285)  that  every  other  brush  is 
positive  and  is  connected  to  the  positive  terminal  of  the 
machine. 


QUESTIONS 

1.  If  a  person  stands  facing  in  the  direction  of  the  magnetic  flux,  and 
thrusts   downward   a  wire  which  he  holds  in  his  two  hands,  in  which 
direction  is  the  induced  e.  m.  f .  ? 

2.  What  are  the  three   factors  which   determine   the   voltage   of  a 
dynamo?    How  does  each  affect  the  voltage  ? 

3.  How  many  revolutions  per  minute   (r.  p.  m.)  would  a  single-coil 
bipolar  dynamo  have  to  make  in  order  that  the  current  might  have  120 
alternations  per  second  ? 

4.  How  manV  revolutions  per  minute  would  an  eight-pole  generator 
have  to  make  to  have  the  current  alternate  120  times  a 

second? 

5.  Why  are  carbon  blocks  generally  used  instead  of 
copper  brushes  ? 

324.    Excitation  of  the  field  of  generators. 

In  the  magneto  (Fig.  286)  the  magnetic  field 
is  supplied  by  permanent  steel  magnets.  In 
most  other  generators,  the  magnetic  field  is 
furnished  by  powerful  electromagnets.  Some- 
times the  current  needed  to  excite  these  mag- 
nets is  supplied  by  some  outside  source,  such 
as  a  storage  battery,  but  generally  the  machine 
itself  furnishes  the  exciting  current.  •  There 
are  three  types  of  generators  differing  in  the  method  of  excit- 
ing the  field  coils ;  (1)  series-wound,  in  which  the  whole  cur- 
rent generated  passes  through  the  field  coils  on  its  way  to 


FIG.   286.— 
neto  has 
nent  steel  mag- 
nets. 


328 


PRACTICAL  PHYSICS 


the  external  circuit ;  (2)  shunt-wound,  in 
which  the  field  is  excited  by  diverting  a 
small  part  of  the  main  current,  the  field 
coils  and  the  external  circuit  being  in 
parallel  or  in  shunt ;  and  (3)  compound- 
wound,  which  has  both  a  series  coil  and  a 
shunt  coil. 

In  the  series  generator  (Fig.  287),  the 
field  coils  are  wound  with  a  few  turns  of 

FIG.  287.— Series- wound    large  wire.       When  the  Current  in  the  ex- 
generator  supplying   ternal  circuit  increases,  the  field  is  more 
highly  magnetized,  and  so  a  higher  volt- 
age is   available  to  supply  the   current. 
This  machine  is  used  to  furnish  current 
for  arc  lamps,  which  operate  on  a  constant 
current. 

When  the  field  is  shunt-wound  (Fig. 
288),  the  coils  have  many  turns  of  small 
wire,  for  in  this  case  it  is  desirable  to  di- 
vert as  little  current  as  possible  from  the 
main  circuit,  and  so  the  resistance  of  the 
field  coils  should  be  high.  Such  machines  FIG.  288.— Shunt-wound 
are  run  at  constant  speed.  When  more  generator  supplying 
load  is  thrown  on  the  machine,  that  is,  ^candescent  lamps, 
when  more  lamps  are  turned  on,  so  that 
more  current  is  needed,  the  terminal  volt- 
age drops  a  little.  This  decreases  the 
current  in  the  field  coils  and  still  further 
reduces  the  terminal  voltage.  A  shunt  ma- 
chine, therefore,  cannot  be  used  when  very 
constant  voltage  is  desired. 

This  drop  in  the  terminal  voltage  of  shunt 
generators  under  heavy  loads  can  be  over- 
^   "^     7, i"    come  by  the  use  of  the  compound-wound  gen- 

FIG.  289.  — Compound-  £_.  ...     f 

wound  generator.       erator  (Fig.  289),  which  is  the  one  most 


ELECTRIC  POWER  329 

commonly  used.  Here  the  voltage  is  kept  constant  by  adding 
a  series  coil  of  a  few  turns,  which  tends  to  raise  the  voltage 
when  the  current  increases,  just  as  in  a  series  generator.  If 
the  coils  are  carefully  adjusted,  the  voltage  remains  practi- 
cally constant  at  all  loads. 

325.  Source  of  energy  in  the  dynamo.'  It  is  important  to 
remember  that  the  electric  generator  or  dynamo  can  not  of 
itself  make  electricity,  but  can  only  transform  mechanical  en- 
ergy into  electrical  energy.  For  example,  if  we  want  to  light 
a  house  with  electricity,  it  is  not  enough  for  us  to  buy  a 
dynamo,  we  must  get  also  a  steam  engine,  or  a  gas  engine  or 
a  water  wheel  to  drive  the  dynamo.  We  have  already  seen 
that  the  induced  current  is  always  in  such  a  direction  as  to 
oppose  the  motion  of  the  wire.  Consequently,  the  greater 
the  current  in  the  dynamo,  the  greater  the  power  needed  to 
turn  it.  Large  generators,  such  as  are  used  in  power  sta- 
tions to  furnish  electricity  for  street  railways,  sometimes  re- 
quire steam  engines  of  16,000  to  20,000  H.  P.  capacity. 


ELECTRIC  POWER 

326.  How  electric  power  is  measured.  To  measure  water 
power,  we  must  know  the  quantity  of  water  flowing  per 
minute  and  the  "  head  "  of  the  water.  Thus 

Water  power  =  quantity  of  water  per  minute  x  head. 

H    P   _lb.  per  min.  x  ft. 
33000 

To  measure  electric  power,  we  must  multiply  the  quantity 
of  electricity  flowing  per  second  —  that  is,  the  intensity  of 
the  electric  current  —  by  the  voltage.  Thus 

Electric  power  =  intensity  of  current  x  voltage. 
The  watt  is  the  unit  of  electric  power  and  may  be  defined  as 


330  PRACTICAL   PHYSICS 

the  power  required  to  keep  a  current  of  one  ampere  flowing 
under  a  drop  or  "  head  "  of  one  volt. 

Watts  =  amperes  x  volts. 

Since  the  watt  is  a  very  small  unit  of  power,  we  commonly 
use  the  kilowatt  (K.W.)  which  is  1000  watts. 

v  -..       amperes  x  volts 

Jtv.   W  .  =:  • • 

1000 

Inasmuch  as  mechanical  power  is  reckoned  in  horse  power 
(H.  P.),  it  will  be  convenient  to  know  the  relation  of  the 
unit  of  mechanical  power  to  the  unit  of  electrical  power. 
Experiment  shows  that 

1  horse  power  =  746  watts. 
1  Kilowatt  (K.W.)  =  1.34  horse  power  (H.  P.). 

Since  we  have  to  compute  electrical  power  very  often,  we 
may  find  a  formula  convenient. 

P=IE, 
where  P  =  power  in  watts, 

1=  current  in  amperes, 

E=  e.  m.  f.  in  volts. 

For  example,  if  a  lamp  draws  0.5  amperes  from  a  110  volt  circuit,  it 
is  using  power  at  the  rate  of  0.5  times  110  or  55  watts. 

Again,  suppose  a  street-car  heater  has  a  resistance  of  110  ohms.  At 
what  rate  is  it  consuming  electricity  on  a  550  volt  line  ?  The  current  is 
|-^§  or  5  amperes,  and  the  power  is  5  times  550  or  2750  watts  or  2.75  K.  W. 

327.  Commercial  units  of  electrical  work.  Power  means 
the  rate  of  doing  work.  The  total  work  done  is  equal  to  the 
product  of  the  rate  of  doing  work  by  the  time.  Thus  if  a  steam 
engine  is  working  at  the  rate  of  15  horse  power  for  8  hours, 
it  does  8  times  15  or  120  horse-power  "hours  of  work.  In  a 
similar  way,  if  an  electric  generator  is  delivering  electricity 
at  the  rate  of  15  kilowatts  for  8  hours,  it  does  8  times  15  or 
120  kilowatt  hours  of  work. 


ELECTRIC  POWER  331 

For  example,  we  buy  electricity  by  the  kilowatt  hour.  In  Boston  the 
price  is  about  10  cents  per  kilowatt  hour.  If  a  store  uses  100  lamps  for 
3  hours,  each  consuming  electricity  at  the  rate  of  50  watts,  it  will  cost 

100  x  3  x  50  x  0.10 
1000 

328.  Small  units  of  electrical  work.  In  the  laboratory  we 
often  find  it  convenient  to  use  a  smaller  unit  of  work,  the 
watt  second  or  joule. 

Work  (joules)  =  current  (amperes)  x  e.  m.  f.  (volts)  x  time  (seconds). 

Or  W  =  lEt, 

since  1  Kilowatt-hour  =  3,600,000  watt  seconds  or  joules, 

1  Horse-power  hour  =  1,980,000  foot  pounds. 
Therefore  1  joule  =  0.74  foot-pounds. 


PROBLEMS 

1.  How  much  electrical  power  (watts)  is  required  to  light  a  room 
with  5  lamps,  if  each  lamp  draws  0.4  amperes  from  a  110-volt  line? 

2.  A  street  railway  generator  is  delivering  current  to  a  trolley  line 
at  the  rate  of  1500  amperes  and  at  550  volts.     At  what  rate  (kilowatts) 
is  it  furnishing  power? 

3.  How  many  horse  power  will  be  required  to  drive  the  generator  in 
problem  .2,  if  its  efficiency  is  90%? 

4.  A  10  kilowatt  generator  is  working  at  full  load.     If  the  voltmeter 
reads  115  volts,  how  much  does  the  ammeter  read? 

5.  How  many  lamps,  each  of  120  ohms  and  requiring  1.1  amperes, 
can  be  lighted  by  a  25  K.  W.  generator? 

6.  How  much  power  is  required  by  a  laundry  using  5  electric  flat- 
irons  of  50  ohms  each  on  a  110-volt  line? 

7.  How  much  will  it  cost  at  10  cents  per  kilowatt  hour,  to  run  a  220- 
volt  motor  for  10  hours,  if  the  motor  draws  25  amperes  ? 

8.  Would  it  be  cheaper  to  buy  the  power  needed  in  problem  7  at  8 
cents  per  horse-power  hour  ? 

9.  How  much  energy  is  consumed  in  a  line  whose  resistance  is  0.5 
ohms,  and  which  carries  a  current  of  150  amperes  for  10  hours? 

10.    How  many  joules  of  energy  are  consumed  when  a  40- watt  lamp 
burns  10  minutes  ? 


332 


PRACTICAL   PHYSICS 


ELECTRIC  HEATING 

329.  Heating  by  electricity.     We  are  familiar  with  the 
fact  that  electric  cars  are  heated  by  electricity,  and  that  an 

electric  light  bulb  gets  hot,  and  we  may 
have  used  or  seen  electric  flatirons  (Fig. 
290),  electric  ovens,  or  electric  furnaces ; 
but  perhaps  we  do  not  realize  that  every 
electric  current,  however  small,  gener- 
ates heat.  This  is  because  heat  is  gen- 
erated so  slowly  in  an  electric  bell,  tele- 
graph, or  telephone,  that  it  is  radiated 
off  without  raising1  the  temperature  of 

FIG.   290.  —  Flatiron       .  .  °.  ,  ,     . r  ,,  . 

heated  by  electricity,    tn^  wires  appreciably.      It  is  this  heat- 
aud  the  resistance  wire    ing  effect  which  limits  the  output  of  a 

in  it  shown  separately.     generator>  for  if  too  heavy  a  Clirrent  is 

drawn  from  the  machine,  the  armature  and  field  coils  get  so 
hot  that  the  insulation  is  set  on  fire. 

330.  Fuses   and   circuit  breakers.     To   protect   electrical 
machines  from   too  much 

heat  caused  by  excessive  cur- 
rent, some  sort  of  "electrical 
safety  valve  "  has  to  be  in- 
serted in  the  circuit.  Fuses 
are  used  for  the  small  cur- 
rents in  house  lights  and 
small  motors,  and  circuit 
breakers  for  larger  currents 
in  power  stations.  The  es- 
sential part  of  a  fuse  is  a 
strip  of  an  alloy  [Fig.  291 
(a)],  which  melts  at  such  a 
low  temperature  that  the 
melted  metal  can  do  no  . 

.  .  .  FIG.  291.— Fuses:  (a)  wire  fuse;  (6)  car- 

narm.      ine  size  01  trie  iuse  tridgefuse;  (c)  plug  fuse. 


ELECTRIC  POWER 


333 


FIG.  292.  — Circuit  breaker. 


is  such  that  if  by  accident  too  heavy  a  current  is  sent  through 
the  wires,  the  fuse  melts  and  breaks  the  circuit.  At  the  mo- 
ment the  fuse  melts  there  is  an  arc  across  the  gap  which 
might  set  things  on  fire.  So  the  fuse 
is  commonly  inclosed  in  an  asbestos 
tube,  as  in  the  "  cartridge  fuse " 
[Fig.  291  (&)],  or  in  a  porcelain  cup, 
which  screws  into  a  socket  like  a 
lamp,  as  in  the  "  plug  fuse "  [Fig. 
291  (<?)].  When  the  fuse  wire  melts 
because  of  excessive  current,  the  fuse 
is  said  to  "blow  out." 

A     circuit   breaker    (Fig.    292)     is 
simply    a     large     switch     which    is 
automatically  opened    by    an  electromagnet  when  the  cur- 
rent is  excessive. 

331.    How  much  heat  is  generated  by  an  electric  current? 
The  energy  delivered  to  an  electric  heating  coil,  such  as  a 

flatiron,  or  soldering  iron,  is,  as  we 
have  seen  in  section  326,  El  joules 
per  second,  or  Elt  joules  in  t  seconds. 
But  since  Ohm's  law  tells  us  that  E  = 
IR,  if  there  is  no  cell,  generator, 
or  motor  in  the  part  of  the  circuit 
considered,  we  have  the  alternative 
statement,  which  is  often  more 
\Miye  convenient  in  discussing  electric 
heaters  :  — 

ffi  Energy  turned  into  heat  =  I*Rt  (joules). 

To  measure  the  heat  generated  by 

FIG.  293.  — The  electromagnet  i      ,    • 

in  the  circuit-breaker  in  Fig-    an   electric   current   m   a    wire,    we 
ure  292.   This  type  is  used    can  let  it  raise  the  temperature  of 

for  very  large  currents^and     a   known   weight  of  Water.       Careful 

wire  on  the  electromagnet,      experiments  show  that  a  current  of 


334  PRACTICAL  PHYSICS 

one  ampere  flowing  through  a  wire  of  one  ohm  resistance  foi 
one  second  will  generate  enough  heat  to  raise  the  tempera- 
ture of  one  gram  of  water  0.24°  C.  That  is, 

H  =  0.24  I*Rt, 

where  H=  heat  in  calories, 

I  =  current  in  amperes, 
R  =  resistance  in  ohms, 
t  =  time  in  seconds. 

PROBLEMS 

1.  How  many  calories  of  heat  are  generated  per  hour  in  a  30  ohm 
electric  flatiron  using  4  amperes  ? 

2.  What  is  the  cost  of  each  calorie  in  problem  1,  if  the  electricity 
costs  10  cents  per  kilowatt  hour  ? 

3.  How  much  energy  is  turned  into  heat  each  hour  by  a  current  of 
35  amperes  in  a  wire  of  resistance  2  ohms?     What  size  rubber-covered 
copper  wire  should  be  used  to  carry  this  current  safely?     (See  table  at 
end  of  Chapter  XVJ.) 

4.  If  88  %  of  the  energy  received  by  an  electric  lamp  is  converted  into 
heat,  how  many  calories  are  developed  in  one  hour  by  a  35  candle  power 
lamp  drawing  0.9  amperes  at  115  volts? 

5.  A  10  ohm  coil  of  wire  is  used  to  heat  1000  grams  of  water  from 
15°  C  to  75°  C  in  10  minutes.     How  much  current  must  be  used? 

6.  How  long  will  it  take  5  amperes  at  55  volts  to  raise  the  tempera- 
ture of  a  kilogram  of  water  from  20°  to  100°  C  ? 

ELECTRIC  LIGHTING 

332.  The  electric  arc.  About  a  hundred  years  ago  Sir 
Humphrey  Davy  (1778-1829),  by  using  a  battery  of  2000 
cells,  made  an  electric  arc  between  rods  of  charcoal.  This 
was  merely  a  brilliant  lecture  experiment,  and  it  was  not 
until  sixty  years  later,  when  practical  dynamos  had  been 
built,  that  arc  lights  became  commercially  possible.  It  was 
soon  found  that  the  coke  which  is  formed  in  the  ovens  of  gas 
furnaces  makes  a  more  durable  material  for  the  carbon  than 
wood  charcoal. 


ELECTRIC  POWER 


335 


To  show  the  form  of  the  electric  arc  we  may  connect  a  current  of 
50  or  more  volts  to  two  carbons,  in  series  with  a  suitable  rheostat.  The 
light  is  so  intense  that  the  eyes  must  be  shielded 
by  blue  glass  from  the  direct  glare.  The  arc  can 
be  projected  on  a  screen  with  a  convex  lens.  If 
D.  C.  current  is  used,  .the  crater  formed  on  the 
positive  carbon  and  the  cone  on  the  negative  car- 
bon can  be  seen  as  shown  in  Fig.  294.  The  great 
heat  evolved  is  shown  by  the  fact  that  iron  wire' 
can  be  melted  in  the  arc. 


FIG.  294.— Positive  and 
negative  carbons  of 
the  arc. 


Out* 


Furnaces  built  on  the  principle  of  the 
electric  arc  are  used  to  prepare  artificial 
graphite,  carborundum,  calcium  carbide, 
and  various  kinds  of  steel. 

333.  Modern  arc  lamps.  Even  coke 
carbon  burns  away,  and  so  automatic 
lamps  have  been  invented  which  feed 
their  carbons  gradually  toward  each 
other.  Some  of  the  early  forms  of  these 
lamps  made  use  of  clockwork  to  feed  the  carbons,  but  now 
it  is  common  to  use  a  clutch  which  is  worked  by  an  electro- 
magnet. One  form  of  this  mechanism  consists  of  a  "  bal- 
lasting" resistance  B  (Fig. 
295),  which  opposes  any  in- 
crease or  decrease  of  current 
between  the  carbon  tips,  and 
of  a  "  regulating "  coil  $,  to 
control  the  distance  between 
the  carbon  tips.  When  there 
is  no  current,  the  plunger  P 
drops  and  releases  the  friction 
clutch  on  the  upper  carbon  O. 
When  the  current  is  on,  the 
plunger  P  is  pulled  up  and 

FIG.  295. -Arc  lamp,  and  diagram  of     lifts     the     clutch     and     UPP6r 

automatic  feed.  carbon  the  proper  distance. 


336 


PRACTICAL  PHYSICS 


Recently  an  inclosed  arc  lamp  (Fig.  296)  has  come  into 
general  use.  When  the  arc  is  surrounded  by  a  glass  globe 
which  is  nearly  air-tight,  the  available  supply 
of  oxygen  is  quickly  used  up  and  the  same 
pair  of  carbons  lasts  100  hours  instead  of 
only  7  or  8  hours. 

If  the  carbon  rods  are  made  with  a  core  of 
calcium  fluoride,  the  vapor  given  off  is  very 
luminous  and  gives  a  light  of  a  golden 
FIG.  296.—  inclosed  orange  color.  These  so-called  flaming  arcs 
are  extensively  used  on  streets  for  advertis- 
In  this  type  the  carbons  are 


arc  lamp. 


mg  purposes. 


feed 


FIG.  297. —  Impreg- 
nated carbons  of 
flaming  arc. 


long   and   slender,   and    both   carbons 
down,  as  shown  in  figure  297. 

Another  form  of"  flaming  arc  is  the  mag- 
netite arc.  In  this  lamp  the  lower  electrode 
is  made  of  magnetite  or  some  similar  sub- 
stance, powdered  and  compressed  in  a  sheet- 
iron  tube,  while  the  upper  electrode  is  of 
solid  copper  which  wastes  away  very  little. 

In  the  mercury  arc  or  Cooper- Hewitt 
lamp,  use  is  made  of  the  luminescence  of  mercury  vapor. 

The  mercury  is  held  in 
the  lower  end  of  a  glass 
vacuum  tube  2  to  4  feet 
long  (Fig.  298).  Some 
special  device  has  to  be 
used  to  start  the  current 
through  the  mercury 


vapor;  but  once  started, 
the  current  flows  easily 
through  the  hot  vapor, 
which  glows  with  a  light 

Fm.  298. -Mercury  arc  lamp,  started  by      CO™Posed   of    Sreen'   b'lue' 

tilting.  and   yellow,  but   no  red. 


ELECTSIC  POWER  337 

This  gives  a  peculiar  color  to  objects  thus  illuminated.     (See 
Chapter  XXIII.) 

334.  Carbon  filament  lamps.     In  incandescent  lamps,  there 
is  a  wire  or  filament  which  is  heated  white  hot  by  the  electric 
current.     The  light  emitted  is  the  same  as  it  would  be  if  the 
same  wire  could  be  heated  to  the  same  temperature  in  any 
other  way,  as  by  an  oxyhydrogen  flame.     In  the  early  ex« 
periments  platinum  was  tried  for  the  filament, 

but  even  though  its  melting  point  is  as  high 
as  1600°  C,  it  could  not  stand  the  temperatures 
required.      Carbon  is  one  of  the  few  known 
substances  with  a  higher  melting  point,  and  in 
1880  Edison  and  others  succeeded  in  making  a 
lamp  with  a  carbon  filament.      Since  the  fila-    FIG.  299.— Gar- 
ment would  burn  up  at  once  if  there  were  any       *>on  filament 
air  present  to  support  the  combustion,  it  has  to 
be  inclosed  in  a  glass  bulb  (Fig.  299)  in  which  there  is  a 
very  high  vacuum. 

The  electricity  is  led  into  and  out  of  the  filament  through 
two  short  platinum  wires,  melted  into  the  glass  bulb  at  one 
end.  These  platinum  wires  are  connected  by  copper  wires 
to  the  brass  collar  and  metal  tip  at  the  end  of  the  bulb. 
Such  lamps  are  usually  made  for  110  or  220  volts.  If  a 
lamp  made  for  110  volts  is  used  on  a  105  volt  line,  it  will 
probably  last  twice  as  long,  but  will  only  give  80%  as  much 
light.  If  it  is  used  on  a  113  volt  line,  even  though  it  gives 
about  18%  more  light,  it  will  last  only  half  as  long.  So  it 
is  very  desirable  to  use  lamps  on  the  voltage  for  which  they 
are  intended.  This  means  we  must  have  good  regulation  on 
the  electric  lighting  service ;  that  is,  constant  voltage  at  all 
loads. 

335.  Commercial  rating  of  electric  lights.     To  measure  the 
output  of  light  from  a  lamp,  we  need  some  standard  lamp  for 
comparison.     As  will  be   explained  in   Chapter  XXI,   this 
standard  is   the  so-called  international  candle.     The  ordinary 


338  PRACTICAL  PHYSICS 

incandescent  light  is  equivalent  to  about  16  such  standard 
candles,  and  it  said  to  be  16  candle  power  (16  c.p.).  Since 
lamps  do  not  show  the  same  brightness  on  all  sides,  it  is 
customary  to  take  the  average  candle  power  in  all  directions 
in  a  horizontal  plane.  Thus  incandescent  lamps  are  often 
rated  according  to  their  mean  horizontal  candle  power. 

The  input  of  electrical  energy  is  measured  in  watts.  The 
commercial  rating,  which  is  also  called  the  "  efficiency"  *  of  elec- 
tric lamps  is  the  number  of  watts  per  candle  power.  For 
example,  an  ordinary  50  watt  lamp  gives  16  candle  power ; 
so  its  commercial  rating  is  -|J  or  3.1  watts  per  candle  power. 
By  a  special  firing  process,  carbon  filaments  can  be 
"  metallized  "  The  efficiency  of  such  filaments  is  about 
2.5  watts  per  candle  power. 

336.    Metal  filament    lamps.     Still   more   efficient   incan- 
descent lamps  are  made  with  metallic  filaments.     The  metals 
most  used  are  tantalum  and  tungsten,  both 
of  which  have  melting  points  much   higher 
than  that  of  platinum.     Since  their  specific 
resistance  is  much  lower  than  that  of  carbon, 
a  metal  filament  must  be  very  much  longer 
and  thinner  (about   0.02  millimeters   in  di- 
ameter) than  a  carbon  filament  to  have  the 
FIG  soo  —Metal    necessarv  resistance.     So  long  a  wire  can  be 
filament  lamp.      put  in  a  bulb  of  the  ordinary  size  only  by 
"  winding   it   zigzag  on  star-shaped    reels,   as 
shown  in  figure  300. 

One  difficulty  with  these  metal  filaments  is  their  brittle- 
ness  and  liability  to  breakage.  Furthermore,  they  soften 
somewhat  when  hot,  and  if  a  metal-filament  lamp  is  used  in 
a  horizontal  position,  the  filament  may  sag  and  short-circuit. 
Nevertheless,  the  extremely  high  efficiency  of  these  lamps, 
their  long  life  (except  for  breakage),  and  their  wonderful 

*This  is  really  a  measure  of  inefficiency ;  the  larger  the  number  the  worse 
the  lamp. 


ELECTRIC  POWER 


339 


white  light,  which  is  the  same  color  as  daylight,  have  made 
them  very  popular. 

COMPARATIVE  "  EFFICIENCY  "  OF  ELECTRIC  LAMPS 


NAME  OF  LAMP 

WATTS  PER 
CANDLE 
POWER 

NAME  OF  LAMP 

WATTS  PER 
CANDLE 
POWER 

Carbon  filament     .     . 
Metallized  carbon 
Tantalum  

3  to  4 
2.5 
20 

Arc  lamp 
Mercury  arc 
flaming  arc 

0.5  to  0.8 
0.6 
0.4 

Tungsten 

1  0  to  1  5 

QUESTIONS  AND  PROBLEMS 

1.  Why  must  a  rheostat  be  used  in  series  with  the  arc  lamp  in  a  pro- 
jection lantern  ? 

2.  Why  are  the  flaming  arc  lamps,  which  are  used  for  street  lighting, 
placed  high  above  the  street  ? 

3.  When  an  incandescent  light  bulb  gets  very  hot  and  blackens  on 
the  inside,  what  does  it  indicate? 

4.  What  must  be  the  voltage  of  an  arc-lighting  dynamo  which  is  to 
furnish  8  amperes  to  25  street  lamps  arranged  in  series,  if  each  lamp  re- 
quires a  terminal  voltage  of  50  volts? 

5.  What  would  be  the  kilowatt  output  of  the  generator  in  problem  4  ? 

6.  How  may  a  street  car,  which  is  operated  on  a  550  volt  line,  be 
lighted  by  110  volt  lamps?     Draw  a  diagram  of  the  connections. 

7.  In  considering  the  proper  kind  of  electric  lamp  for  illumination, 
what  other  factors  must  be  considered  besides  watts  per  candle  power  ? 

8.  How  many  0.5  ampere  lamps,  connected  in  parallel,  can  be  pro- 
tected by  a  20-ampere  fuse  ? 

9.  How  many  candle  power  should  a  50  watt  tungsten  lamp  give,  if 
its  efficiency  is  1.2  watts  per  candle  power? 

10.  It  was  found  on  testing  a  32  candle  power  lamp  that  it  consumed 
100  watts  of  electric  power,  of  which  88  watts  were  turned  into  heat. 
What  was  its  efficiency  for  heating?  What  was  its  light  efficiency  in 
the  true  sense?  What  was  its  commercial  rating? 


340 


PRACTICAL  PHYSICS 


ELECTRIC  MOTOR 

337.  The  dynamo  as  a  motor.     We  have  already  seen  that 
a  dynamo,  when  driven  by  a  steam  engine,  gas  engine,  or 
water  wheel,  may  generate  electricity.     Now  wre  shall  see 
how  this  electric  current  can  be  supplied  to  a  second  machine, 
exactly  like  a  dynamo,  but  called  a  motor,  which  may  be  used 
to  drive  an  electric  car,  a  printing  press,  a  sewing  machine, 
or  any  other  machine  requiring  mechanical  energy.     In  short, 
the  dynamo  is  a  reversible  machine,  and  sometimes  in  shops, 
and  often  on  self-starting  automobiles,  the  same  machine  is 
driven  as  a  generator  part  of  the  time,  and  used  as  a  motor 
to  drive  another  machine  the  rest  of  the  time. 

Structurally,  the  motor,  like  the  dynamo,  consists  of  an 
electromagnet,  an  armature,  and  a  commutator  with  its 
brushes.  To  understand  how  these,  act  in  the  motor,  how- 
ever, we  must  get  a  clear  idea  of  the  behavior  of  a  wire 
carrying  an  electric  current  in  a  magnetic  field. 

338.  Side  push  of  a  magnetic  field  on  a  wire  carrying  a  cur- 
rent.    We  will  stretch  a  flexible  conductor  loosely  between  two  binding 


FIG.  301.  —  Side  push  on  wire  carrying  a  current. 


posts  A  and  B,  so  that  a  section  of  the  conductor  lies  between  the  poles 
of  an  electromagnet,  as  shown  in  figure  301.  Let  the  exciting  current 
be  so  connected  to  the  electromagnet  that  the  poles  are  ^and  S  as  shown. 
Then,  if  a  strong  current  from  a  storage  battery  is  sent  through  the  con- 
ductor from  A  to  B  by  closing  the  key  K,  it  will  be  seen  that  the  wire. 


ELECTRIC  POWER 


341 


with  current  going 
in. 


between  the  magnet's  poles  is  instantly  thrown  upward.  If  the  current 
is  sent  from  B  to  A,  the  motion  of  the  conductor  is  reversed,  and  it  is 
thrown  doivnward. 

It  will  help  us  to  understand  this 
side  push  exerted  on  a  current-carrying 
wire  in  a  magnetic  field,  if  we  recall 
that  every  current  generates  a  magnetic 
field  of  its  own,  the  lines  of  which  are 
concentric  circles.  Figure  302  shows  a 
wire  carrying  a  current  w,  that  is,  at 
right  angles  to  the  paper  and  away  from  us.  The  lines 
of  force  are  going  around  the  wire  in  clockwise  direc- 
tion. 

The  magnetic  field  between  the 
poles  of  a  strong  magnet  is  practi- 
cally uniform  and  is  represented 
by  parallel  lines  of  force  shown  in 
figure  303. 

If  we  put  the  wire,  with  its  cir- 
cular field,  in  the  uniform  field  be- 


FIG.  303.  "Uniform  magnetic 

tween   the  N  and  S  poles  of  the 

magnet,  the  lines  of  force  are  very  much  more  crowded 
above  the  wire  (Fig.  304)  than  below.  But  we  have  seen  in 
section  238  that  we  can  think  of  magnetic  lines  of  force  as  act- 
ing like  rubber  bands  which  would, 
in  this  case,  push  the  wire  down. 
If  the  current  in  the  wire  is  re- 
versed, the  crowding  of  the  lines 
of  force  comes  below  the  wire,  and 
it  is  pushed  up. 

339.    Motor  rule  of  three  fingers. 
The  rule   for  remembering   which 


FIG.  304.  —  Lines  of  force  about 
a  wire  carrying  current  in  a 
magnetic  field. 


way  this  side  push  on  a  wire  in  a  magnetic  field  will  move 
the  wire  is  precisely  the  same  as  that  for  the  generator 
except  that  the  left  hand  instead  of  the  right  is  used. 


342 


PRACTICAL  PHYSICS 


FIG.  305.  — Drum-wound  motor. 


340.  The  action  of  a  motor.     In  motors,  as  in  dynamos, 
the  drum  type  of  armature  is  almost  exclusively  used.     It 
will  be  remembered  (see  section  322)  that  in  this  type  the 
active  wires  lie  in  slots  along  the  outside  of  the  drum,  as  in 

figure  305,  and  the  wiring  con- 
nections across  the  ends  of  the 
armature  are  such  that  when 
the  current  is  coming  out  on  one 
side,  —  say  the  right,  —  it  will  be 
going  in  on  the  other  side  —  the 
left.  Just  how  these  wiring  con- 
nections are  made  is  not  important 
for  the  present  purpose,  and  in- 
deed there  are  many  different  ways  in  which  they  can  be  ar- 
ranged. In  any  case,  from  what  has  just  been  said,  it  will  be 
clear  that  the  wires  (O)  on  the  right  side  of  the  armature 
will  be  pushed  upward,  and  those  (0)  011  the  left  side  of  the 
armature  will  be  pushed  downward  by  the  magnetic  field. 
In  other  words,  there  will  be  a  torque  tending  to  rotate  the 
armature  counter-clockwise.  The  amount  of  this  torque  de- 
pends on  the  number  and  length  of  the  active  wires  on  the 
armature,  on  the  current  in  the  armature,  and  on  the  strength 
of  the  magnetic  field. 

Another  way  of  lookirfg  at  this  action  is  to  notice  that 
the  effect  of  these  armature  currents  is  such  as  to  make  the 
armature  core  a  magnet,  with  its  north  pole  at  the  bottom 
and  its  south  pole  at  the  top.  The  attractions  and  repulsions 
between  these  poles  and  those  of  the  field  magnet  cause  the 
armature  to  rotate  as  indicated  by  the  arrows. 

The  function  of  the  commutator  and  brushes  is,  as  in  the 
generator,  to  reverse  the  current  in  certain  coils  as  the 
armature  rotates,  so  as  to  keep  the  current  circulating,  as 
shown  in  figure  305. 

341.  Forms  of  motors.     D.C.  generators  and  motors  are 
often  of  identical  construction.     Thus  we  have  series  motors, 


ELECTRIC  POWEE  343 

such  as  are  used  on  street  cars  and  automobiles,  and  shunt 
motors,  such  as  are  used  to  drive  machinery  in  shops.  So 
also  we  have  bipolar  and  multipolar  motors.  When  it  is  de- 
sirable that  a  motor  shall  run  at  a  slow  speed,  it  is  built  with 
a  large  number  of  poles. 

342.  Back  e.  m.  f .  in  a  motor.    Suppose  we  connect  an  incandescent 
lamp  in  series  with  a  small  motor.     If  we  hold  the  armature  stationary, 
and  throw  on  the  current  from  a  battery,  the  lamp  will  glow  with  full 
brilliancy,  but  when  the  armature  is  running,  the  lamp  grows  dim. 

This  shows  that  a  motor  uses  less  current  when  running 
than  when  the  armature  is  held  fast.  The  electromotive  force 
of  the  battery  and  the  resistance  of  the  circuit  are  not 
changed  by  running  the  motor.  Therefore,  the  current 
must  be  diminished  by  the  development  of  a  back  electromotive 
force,  which  acts  against  the  driving  e.  m.  f . 

Since  a  motor  has  a  series  of  armature  wires  cutting  mag- 
netic lines  of  force,  it  is  bound  to  generate  an  e.m.  f.  in  these 
wires.  That  is,  every  motor  is  at  the  same  time  a  dynamo. 
The  direction  of  this  induced  e.  m.f.  will  always  be  opposite 
to^that  driving  the  current  through  the  motor. 

Just  as  in  the  generator,  when  the  armature  revolves 
faster,  the  back  e.  m.  f .  is  greater,  and  the  difference  between 
the  impressed  e.  m.  f.  and  the  back  e.  m.  f .  is  therefore  smaller. 
This  difference  is  what  drives  the  current  through  the  re- 
sistance of  the  armature.  So  a  motor  will  draw  more  current 
when  running  slowly  than  when  running  fast,  and  much 
more  when  starting  than  when  up  to  speed. 

For  example,  suppose  the  impressed  or  line  voltage  on  a  motor  is  110 
volts,  and  the  back  e.m.  f.  is  105  volts.  Then  the  net  voltage  which  will 
force  current  through  the  armature  is  110  —  105,  or  5  volts.  If  the  arma- 
ture resistance  is  0.50  ohms,  the  armature  current  is  5.0/0.5,  or  10  am- 
peres. But  if  the  whole  voltage  (110  volts)  were  thrown  on  the  arma- 
ture while  at  rest,  the  current  would  be  110/0.5  or  220  amperes. 

343.  Starting  a  motor.     When  a  motor  starts  from  rest, 
there  is,  of  course,  no  back  e.  m.  f .  at  first,  and  if  the  motor 


344 


PRACTICAL  PHYSICS 


is  thrown  directly  on  the  line,  there  will  be  such  an  exces- 
sive current  as  to  "  burn  out "  the,  armature.  To  prevent 
this  first  rush  of  current,  a  starting  resistance  is  put  into  the 
circuit  at  first,  and  cut  out  step  by  step  as  the  machine  speeds 

up.  The  device  for  doing 
this  is  shown  in  figure  306. 
See  also  figure  257. 

344.  Applications  of  the 
motor.  The  transmission  of 
power  through  shops  and 
factories  by  means  of  shaft- 
ing, cables,  and  belts  is 
dangerous,  noisy,  and  un- 
economical. In  a  modern 
system,  electric  power  is 
generated  in  a  central  power 
house,  is  transmitted  to  va- 
rious parts  of  the  plant, 
and  is  used  in  electric 

F,G.306.-Motor  with  staTn'g  resistance.     mOt°rS   t()  d"Ve  eith<*   indi- 

vidual   machines  or   groups 

of  machines.  When  electrical  transmission  is  used,  the 
danger  and  inconvenience  of  belts  and  shafting  are  avoided, 
the  machines  can  be  set  in  any  position,  and  their  speed  can 
be  easily  controlled  by  field  rheostats.  In  shops  and  factories 
thus  equipped,  shunt  motors  are  commonly  used,  for  constant 
speed  motors  are  required,  and  the  speed  of  a  shunt  motor 
under  no  load,  or  a  light  load,  is  nearly  the  same  as  at  full 
load. 

Series  motors  are  used  on  cranes,  automobiles,  and  electric 
cars,  because  this  type  of  motor  has  a  large  starting  torque. 
The  torque  in  a  series  motor  is  proportional  to  the  square 
of  the  current,  while  in  a  shunt  motor  it  is  directly  propor- 
tional to  the  current.  The  fact  that  the  torque  in  a  series 
motor  is  largest  when  the  speed  is  slowest  (because  there  is 


ELECTRIC  POWER 


345 


little  back  e.m.  f.)  makes  it  just  the  kind  of  motor  for  crane 

or  vehicle  work.      When  the  load  on  a  series  motor  drops  to 

zero,  the  motor  may  "  race " ;  that  is,  go  faster  and  faster 

until     the     armature     flies     to 

pieces.      For  this  reason,  series 

motors     are     connected,    either 

directly  (on  same  shaft)  or  by 

cogwheels,  to  the   machines  to 

bs    driven,    so    that    they    can 

never  escape  their  load. 

Figure  307  shows  a  street- 
car motor  with  its  case  lifted 
to  show  the  inside  arrangement. 
The  field  consists  of  four  short 
poles  projecting  from  the  case, 
which  serves  both  to  protect  the 
motor,  and  as  a  path  for  the 
magnetic  flux.  The  armature 
revolves  so  rapidly  that  its 
speed  has  to  be  reduced  by  a  pair  of  cogwheels,  the  larger  of 
which  is  on  the  axle  of  the  driving  wheels,  and  is  not  shown 
in  the  picture.  These  make  the  speed  of  the  axle  about  one 
fourth  that  of  the  motor. 

Street  cars  are  usually  operated  on  a  direct-current  system. 
A  large  multipolar  compound-wound  generator  (Fig.  308) 
at  the  power  station  maintains  about  550  volts  between 
the  trolley  or  third  rail  and  the  track.  A  "  feeder  "  or  cable 

of  low  resistance 
is  run  parallel  to 
the  trolley  wire 
and  connected 
FIG.  308.  —  General  scheme  of  a  trolley  line.  ^o  ft  a^  inter- 

vals, to  avoid  a  large  voltage  drop  in  the  line  when  a 
number  of  cars  are  taking  current  at  a  distance  from  the 
power  plant.  The  current  passes  down  the  trolley  pole 


FIG.  307.  -  Street-car  motor  with  toj 
of  case  lifted  up. 


346 


PRACTICAL  PHYSICS 


Armature 


Armature 


field 


Rail 
Parallel 


into   the   controller   (Fig.  309).       This  is  an  ingenious   ar- 
rangement of  switches  by  which  the  motorman  can   start 

Trolley Trolley his  car  with  both  motors 

in  series  and  with  the 
starting  resistance  all  in; 
then  by  moving  a  lever 
he  gradually  cuts  out  the 
starting  resistance  and 
finally  throws  both  the 
motors  in  parallel,  as 
shown  in  figure  310. 
Thus,  when  starting, 
each  motor  receives  less 
than  half  the  line  volt- 
age, and  when  running 
at  full  power,  gets  full 
voltage.  The  current 
leaves  the  motors  by  the 
wheels,  and  goes  back  to 
the  power  station  through  the  rails. 

345.  Efficiency  of  the  electric  motor.  One  reason  for  the 
extensive  use  of  electric  motors  is  their  great  efficiency, 
sometimes  as  high  as  80  %  or  90  %.  The  efficiency  of  a  motor, 
just  as  of  any  machine,  means  the  ratio  of  out-put  to  in-put. 
We  can  easily  measure  the  number  of  amperes  and  the  num- 
ber of  volts  supplied  to  the  motor  and  thus  compute  the 
watts  put  in. 

To  get  the  output  of  mechanical  work,  engineers  usually 
make  a  "brake-test."  One  simple  form  of  brake  consists 
of  a  belt  or  cord  attached  to  two  spring  balances  and 
passing  under  a  pulley  on  the  motor  shaft,  as  shown  in 
figure  311. 

If  the  pulley  rotates  as  indicated,  it  is  evident  that  one 
spring  balance  will  have  to  exert  more  force  than  the  other 
because  of  the  friction  of  the  pulley  on  the  cord,  The  amount 


Rail 
Series 

FIG.  310.  — Series-parallel  control  of  electric 
cars. 


CflBUE  STRuNCi    ON   LINE  OF  STflNDBRO  TOWE.RS. 

ST-LOUIS    TRRNSMISSION     LINE        NOV 


FIG.  309  (above  at  left).  —  Street  car  controller. 
FIG.  324  (below  at  right) .  — Transmission  line. 


Direct  Current  Motor  with  field  coils  shown  above. 


ELECTRIC  POWER 


347 


of  friction  is  equal  to  the  difference  between  the  readings  of 
the  two  balances,  and  it  is  exerted  each  minute  through  a  dis- 
tance equal  to  the 
circumference  of 
the  pulley  times 
the  revolutions  per 
minute.  The  work 
done  in  one  minute 
is  equal  to  the 
friction  times  the 
distance  per  min- 
ute. 

Finally,  if  we 
express  the  out- 
put and  input  in 
some  common  unit 

of    power    and    di-     FIG.  311.  —  Measuring  output  of  a  motor  by  means  of 

vide,  we  have  the 

efficiency.     It  will  be  helpful  to  know  that 
1  watt  =  44.3  foot  pounds  per  min.  =  6.12  kilogram  meters  per  min. 

QUESTIONS  AND  PROBLEMS 

1.  Figure  812  represents  a  bipolar  motor  with  the  armature  revolving 
counter-clockwise.  Copy  it  and  indicate  by 
dots  and  crosses  *  in  circles,  the  direction  of 
the  various  currents. 

2.  What  is  the   armature  resistance  of  a 
motor  in  which  the  armature  current  is  4  am- 
peres, the  impressed  e.  m.f.  is  115  volts,  and 
the  back  e.m.f.  is  112  volts? 

3.  Find   the   back  e.  m.  f.   in   a   motor  in 
which   the    armature    resistance    is   0.3   ohms, 
the  current  is  15  amperes,  and  the  impressed 
voltage  is  110  volts. 


FIG.  312  — Bipolar  motor. 


*  A  cross  in  a  circle  represents  the  feathers  of  an  arrow  sticking  into  the 
paper,  and  means  current  going  in.  A  dot  in  a  circle  means  a  current  com- 
ing out. 


348 


PRACTICAL  PHYSICS 


4.  How  much  current  will  be  drawn  by  a  motor  whose  efficiency  is 
90%,  when  it  is  developing  5  H.  P.  and  is  connected  to  the  110  volt 
service  ?  « 

5.  When  a  certain  motor  was  tested  by  the  brake  test,  it  took  67 
amperes  at  113  volts  and  developed  8.5  H.  P.     Calculate  its  efficiency. 


CHEMICAL  EFFECTS  OF  ELECTRIC  CURRENTS 

346.  Conduction  by  solutions.  When  an  electric  current 
flows  along  a  copper  wire,  the  wire  becomes  warm  and  is 
surrounded  by  a  magnetic  field.  When  an 
electric  curre-it  flows  through  a  solution  of 
salt  and  water,  the  solution  is  warmed 
and  is  surrounded  by  the  magnetic  field, 
and  it  is  at  the  same  time  decomposed  or 
broken  up.  For  example,  under  certain 
conditions  an  electric  current  will  decom- 
pose brine  into  a  metal,  sodium,  and  a  gas, 
chlorine,  which  are  the  two  elements  com- 
posing salt.  Not  all  liquids  conduct  elec- 
tricity ;  thus  alcohol  and  kerosene  are  non- 
conductors. Bat  all  liquids  which  do 
conduct  electricity  are  more  or  less  decom- 
posed in  the  process. 

347.  Electrolysis  of  water.  Water  (made  slightly 

acid  with  sulphuric  acid)  can  be  decomposed  by  an 

electric  current  in  the  apparatus  shown  in  figure  313. 

The  platinum  electrodes  are  connected  with  a  battery 
C'IG.  313.—  Water  is  or  generator,  giving  at  least  5  or  6  volts.  The  elec- 
into  trode  in  tube  A,  which  is  connected  to  the  positive 
hy-  (  +  )  pole,  is  called  the  anode,  and  the  other  electrode 

jn  £  js  ^he  cathode.  The  current  passes  through  the 
solution  from  the  anode  A  to  the  cathode  B.  Small  bubbles  of  gas  are  seen 
to  rise  from  both  electrodes,  and  the  gas  collects  in  tube  B  twice  as  fast 
as  in  tube  A.  When  tube  B  is  full,  we  open  the  switch,  and  test  the 
collected  gases.  To  test  the  gas  in  tube  B,  we  open  the  stopcock  at  the 
top  and  apply  carefully  a  lighted  match.  This  gas  burns  with  a  pale 


broken    up 
oxygen  and 
drogen. 


ELECTRIC  POWER 


349 


blue  flame  which  shows  it  to  be  hydrogen.  If  we  open  the  stopcock  in 
tube  A  and  bring  a  glowing  pine  stick  near,  it  bursts  into  a  flame,  which 
shows  the  gas  to  be  oxygen. 

Thus  we  see  that  water  is  decomposed  by  electricity  into 
its  constituent  elements,  hydrogen  and  oxygen.  This  pro- 
cess of  decomposing  a  compound  by  means  of  an  electric 
current  is  called  electrolysis. 

348.  Theory  of  electrolysis.      The  theory  of  this  process 
may  be  stated  as  follows:     The  small  quantity  of  sulphuric 
acid   (H2SO4),    when   put  into  the  water,   breaks  up   into 
hydrogen  ions  (2  H+)  and  sulphate  ions  (SO4~  -),  which  have 
positive   and    negative    charges    of  electricity  respectively. 
When  the  current  is  sent  through  the  solution,  the  positive 
hydrogen  ions  (2  H+)  wander  toward  the  cathode  and  the 
negative  sulphate  ions  (SO4~~)  toward  the  anode.     At  the 
cathode,  the  hydrogen  ions  give  up  their  positive  charges  and 
rise  to  the  surface  as  bubbles  of  hydrogen.     At  the  anode, 
the  sulphate  ions  give  up  their  negative  charges  of  electricity 
and   react   with  the  water   (H2O)   to  form  sulphuric' acid 
(H2SO4)  and  to  set  free  oxygen  (O2).     In  this  way  the  sul- 
phuric acid,  which  is  added  to  conduct  the  electricity,  is  not 
used   up,  while  the  water  (2  H2O)  is  broken  into  hydrogen 
(2  R2)  and  oxygen  (O2). 

349.  Electroplating.       We    may 
illustrate  the  process  of  electroplat- 
ing by  the  following  experiment. 


We  will  put  two  platinum  electrodes  in 
a  U-tube  filled  with  copper  sulphate  solu- 
tion (CuSO4),  as  shown  in  figure  314.  After 
the  electric  current  has  passed  through  the 
solution  for  a  few  minutes,  we  find  the 
cathode  is  coated  with  metallic  copper, 
while  the  anode  is  unchanged.  If  we  re- 
verse the  direction  of  the  current,  we  find 
that  copper  is  deposited  on  the  clean  platinum  plate  which  is  now  the 
cathode,  and  the  copper  coating  on  the  anode  gradually  disappears. 


FIG.  314.  —  Electrolysis  of 
copper  sulphate. 


350  PRACTICAL  PHYSICS 

In  this  way  one  metal  can  be  coated  with  another.  For 
example,  articles  of  brass  and  iron,  which  corrode  in  the  air, 
can  be  coated  with  nickel,  which  does  not  corrode.  Similarly, 
much  cheap  jewelry  is  gold  or  silver  plated.  Many  knives, 
forks,  and  spoons  are  silver  plated,  the  best  being  what  is 
called  "triple"  or  "quadruple  plate." 

In  practice  the  process  is  done  in  vats,  as  in  figure  315. 
The  objects  to  be  plated  are  hung  from  one  copper  "  bus  "  bar, 
and  the  metal  to  be  deposited,  in  this 
case  pure  silver,  is  hung  from  the  other 
bar.  The  vat  contains  a  solution  of  the 
metal  to  be  deposited.  For  silver  plat- 
ing a  solution  of  silver  and  potassium 
cyanide  is  used.  The  bar  carrying  the 
FIG.  315. —  Diagram  of  metal  to  be  deposited  is  connected  with 
electroplating  vat.  the  +  terminal  of  a  low- voltage  gener- 
ator and  the  other  bar  to  the  —  terminal.  The  silver  plates  at 
the  anode  dissolve  as  fast  as  the  silver  is  deposited  on  the  cath- 
ode, the  strength  of  the  solution  remaining  unchanged.  When 
the  coating  has  reached  the  proper  thickness,  a  final  process  of 
buffing  and  polishing  gives  the  surface  the  desired  appearance. 
350.  Electrotyping.  One  might  at  first  suppose  tha*-  this 
book  was  printed  from  the  actual  type  which  was  set  up,  but 
that  is  not  the  case.  Most  books  which  are  made  in  large 
numbers  are  printed  from  electrotype  "plates."  A  wax  im- 
pression of  the  page  as  set  up  in  type  is  made  in  such  a  way 
that  every  letter  leaves  its  imprint  on  the  wax  mold.  Since 
the  wax  is  itself  a  non-conductor,  it  has  to  be  coated  with 
graphite.  This  mold  is  then  placed  in  a  solution  of  copper 
sulphate  and  attached  to  the  negative  bus  bar,  so  that  it 
becomes  the  cathode,  while  a  copper  plate  acts  as  the  anode. 
After  the  current  has  deposited  copper  on  the  wax  mold  to 
the  thickness  of  a  visiting  card,  this  shell  of  copper  is  sepa- 
rated from  the  mold  and  "backed  up"  with  type  metal  to 
give  it  the  necessary  strength  for  printing. 


ELECTRIC  POWER  351 

351.  Refining  of  metals.     Copper  as  it  comes  from   the 
smelting  works  is  not  pure  enough  for  some  purposes,  such 
as  making  wires  and  cables  for  carrying  electricity.     So  the 
copper   for   electrical   machinery   is   refined  by  electricity. 
The  crude  copper  is  the  anode,  a  thin  sheet  of  pure  copper 
is  the  cathode,  and  the  solution  is  copper  sulphate.     The 
copper  deposited  by  the  electric  current  is  remarkably  pure. 
The   anode    of   crude    copper   gradually  dissolves,  and  the 
impurities  drop  to  the  bottom  of  the  vat  as  mud.     In  this 
mud  there  is  generally  enough  gold  and  silver  to  pay  the 
expense  of  the  process.     Copper  purified  in  this  way  is  known 
commercially  as  electrolytic  copper. 

352.  Electrochemical  equivalents  of  metals.     Experiments 
show  that  a  given  current  always  deposits  the  same  amount 
of  a  given  metal  from  a  solution  in  a  given  time.     In  fact, 
this  is    so  accurately  true  that   it  is  the   basis  of  the  most 
accurate  method  known  for  calibrating  standard  ammeters 
(see  section  275).     The  amount  of  metal  deposited  by  a 
current  depends  (1)  on  the  strength  of  the  current,  (2)  on 
the  time  it  flows,  and  (3)  on  the  nature  of  the  metal.     The 
definite  quantity  of  a  substance  deposited  per  hour  by  elec- 
trolysis when  one  ampere  is  flowing  through  a  solution  is 
called  the  electrochemical  equivalent  of  the  substance. 


ELECTROCHEMICAL  EQUIVALENTS 

ELEMENT  SYMBOL  GRAMS  PER  AMPERE  HOUR 

Aluminum                            Al  0.337 

Copper                                   Cu  1.186 

Gold                                     Au  3.677 

Hydrogen                              H  0.0376 

Nickel                                   Ni  1.094 

Oxygen                                  O  0.298 

Silver                                    Ag  4.025 


352  PRACTICAL  PHYSICS 


QUESTIONS  AND  PROBLEMS 

1.  To  determine  which  is  the  +  and  which  the  —  pole  of  a  generator, 
two  copper  wires  are  sometimes  connected  to  the  terminals  and  the  bared 
ends  dipped  in  a  glass  of  water.     One  will  soon  turn  dark.     How  does 
this  experiment  show  which  is  the  positive  terminal? 

2.  How  many  grams  of  silver  are  deposited  in  8  hours  from  a  silver 
nitrate  solution  by  a  current  of  5  amperes? 

3.  How  many  liters  of  hydrogen  will  be  generated  by  a  current  of  10 
amperes  in  4  hours?     (A  liter  of  hydrogen  weighs  0.09  grams  under 
standard  conditions.) 

4.  How  many  amperes  will  be  needed  to  deposit  1.5  pounds  of  copper 
per  day  of  24  hours  ? 

5.  How  long  will  it  take  a  current  of  200  amperes  to  refine  a  ton  of 
copper? 

6.  In  calibrating  an  ammeter  the  current  was  allowed  to  run  2  hours 
and  15  minutes,  and  deposited  39.5  grams  of  silver.     What  would  be  the 
reading  of  the  ammeter,  if  correct? 

7.  Two  electroplating  vats  are  arranged  in  series,  one  for  gold  and 
the  other  for  silver.     How  much  gold  is  deposited  while  1  gram  of  silver 
is  being  deposited  ? 

8.  An  electroplater  buys  his  electricity  by  the  kilowatt  hour.     The 
metal  deposited  in  electroplating  is  proportional  to  the  number  of  am- 
pere hours.     Why  does  he  use  as  low  a  voltage  as  possible? 

9.  What  is  meant  by  triple  and  quadruple  plate  ?j 

353.  Storage  battery.     Some  people  think  a  storage  bat- 
tery is  a  sort  of  condenser  where  electricity  is  stored,  but  it 
is  not  that.     In  the  storage  battery,  as  in  any  other  battery, 
the  electrical  energy  comes  from  the  chemical  energy  in  the 
cells.     The  charging  process  consists  in  forming  certain  chemi- 
cal substances  by  passing  electricity  through  a  solution,  just 
as  hydrogen  and  oxygen  are  formed   in  the  electrolysis  of 
water.     In  the  discharging  process,  electricity  is  produced  by 
the   chemical   action   of    the   substances    which   have   been 
formed  in  the  charging  process. 

354.  Lead  Storage  cell.     We  may  make  a  small  lead  storage  cell  by 
putting  two  sheets  of  ordinary  lead  in  a  glass  battery  jar  with  a  very 
dilute  solution  of  sulphuric  acid.     To  charge  it  or  "  form  "  the  plates 


ELECTRIC  POWER 


353 


quickly  we  connect  this  cell  and  an  ammeter  in 
series  with  a  battery  of  three  or  more  cells,  or 
better,  a  generator  of  about  6  volts  {Fig.  316). 
While  the  current  is  passing,  bubbles  of  gas  rise 
from  each  plate.  If,  after  a  few  minutes,  we 
disconnect  the  generator  and  touch  the  wires  of 
a  voltmeter  to  the  lead  terminals,  it  shows  an 
e.  in.  f.  of  about  2  volts.  If  we  then  connect  an 
electric  bell  in  series  with  the  ammeter  and  the 
lead  cell,  the  bell  rings,  which  shows  that  a  cur- 
rent is  produced,  and  the  ammeter  shows  that 

the  current  on  dis- 


Ammeter 


Voltmeter 

Fia.  316.  —  Forming  a 
lead  storage  cell. 


FIG.  317.  —  Commercial  lead 
storage  cell. 


charge  is  opposite  to 
that  used  in  charg- 
ing the  cell.  When  the  plated  are  lifted  out 
of  the  solution  after  charging,  plate  B,  the 
anode,  is  brown,  due  to  a  coating  of  lead  per- 
oxide (PbO2),  and  plate  A,  the  cathode,  is 
the  usual  gray  of  pure  lead  (Pb). 

In  the  commercial  lead  storage 
(Fig.  317)  cell,  the  negative  plates 
are  pure  spongy  lead  (Pb),  the  posi- 
tive are  lead  peroxide  (PbO2),  and 
the  electrolyte  is  dilute  sulphuric 
acid.  In  the  charging  process,  the  pos- 
itive plate,  which  is  dark  brown,  is  coated  with  lead  peroxide, 
and  the  negative,  which  is  gray,  is 
made  into  spongy  lead.  In  the  dis- 
charging process,  both  plates  gradu- 
ally return  to  a  condition  where 
each  is  covered  with  lead  sulphate 
(PbSO4).  This  isshownin  figure  318. 
The  chemistry  o'f  these  changes  can 
be  briefly  described  by  the  equation 

FIG.  318.  —  Discharging  a  lead 

Charge  -< —  ceil. 

Pb02  +  Pb  +  2  H2S04  =  2  PbS04  +  2  H20. 
— >-  Discharge 

2A 


354  PRACTICAL   PHYSICS 

It  will  be  noticed  that  during  the  charging  process  the 
acid  becomes  more  concentrated.  So  the  condition  of  a 
storage  cell  can  be  determined,  at  least  roughly,  by  the  spe- 
cific gravity  of  the  acid.  The  plates  in  the  commercial  lead 
battery  are  either  roughened  and  then  changed  into  the 
proper  active  materials,  lead  peroxide  and  lead,  by  a  chemi- 
cal process,  or  are  punched  full  of  holes  which  are  filled  with 
the  active  material. 

355.  Advantages   and   disadvantages   of  the   storage   cell. 
The  lead  cell  is  heavy  and  expensive,  and  requires  careful 
handling   to   get   an    efficiency  even   as  high  as  75%.     Its 
principal  use  is  not  as  yet  for  automobiles,  but  in  three  other 
fields.     First,  it  is  often  used  to  carry  the  "  peak  "  of  the 
load  of  a  power  station.     In  certain  hours  of  the  day  the 
demand  for  current  is  too  great  for  the  generators  to  carry, 
so  a  large  storage  battery,  which  has  been  charging  while  the 
load  was  light,  is  used  to  help  out  the  generators.     Second, 
many  companies,  which  have  to  furnish  electricity  without 
interruption  or  pay  a  heavy  fine,  use  a  storage  battery  as  a 
reserve  supply  of  electrical  energy.     In  case  of  accident,  the 
storage  battery  can  be  drawn  upon  at  a  moment's  notice. 
Third,  in  some  small  plants  the  load  on  the  generators  is  very 
light  for  a  considerable  time  each  day  or  night.     In  such 
cases  a  storage  battery  is  sometimes  used  to  take  care  of  this 
long-continued  light  load,  and  the  engine  and  generators  are 
shut  down. 

356.  Edison  storage  battery.     Edison  has  invented  a  stor- 
age cell  in  which  the  negative  plate  is  pure  iron  in  a  steel 
frame,  the  positive  plate  is  nickel  oxide,  and  the  solution  is 
caustic  potash.     Since  this  cell  is  intended  for  traction  work, 
great  pains  have  been  taken  to  make  it  light,  strong,  and  com- 
pact.    Instead   of  being  placed  in  a  glass  or  hard-rubber 
tank,  it  has  a  thin  nickel-plated  sheet-steel  case.     In  a  lead 
cell   the  normal   voltage  on  discharge  is  2  volts  ;    in    the 
Edison  cell  it  is  1.2  volts.     For  the  same  capacity  of  output, 


ELECTRIC  POWER  355 

the  Edison  cell  is  about  half  as  heavy  as  the  lead  cell.  As 
the  internal  resistance  of  the  Edison  is  a  little  more  than 
that  of  the  lead  cell,  its  efficiency  is  a  little  lower.  Whether 
or  not  the  Edison  cell  is  going  to  be  better  than  the  lead  cell 
depends  on  its  "  life  "  under  commercial  conditions,  and  this 
is  not  yet  settled. 

QUESTIONS  AND  PROBLEMS 

1.  In  a  trolley  system  the  generator  maintains  565  volts  on  the  line. 
How  many  lead  storage  cells,  each  of  2.1  volts,  will  be  needed  to  help  the 
generator  carry  the  peak  of  the  load  ? 

2.  Storage  cells  are   sold   according  to  their  "capacity"  in  ampere 
hours.     What  "  capacity  "  will  be  required  to  deliver  10  amperes  contin- 
uously for  8  hours? 

3.  Most  manufacturers  of  lead  cells  allow  about  55  ampere  hours  for 
each  square  foot  of  positive  plate  area.     How  large  a  plate  area  will  be 
required  in  problem  2  ? 

4.  If  the  e.  in.  f.  of  a  lead  cell  is  2.3  volts  on  open  circuit,  while  the 
terminal  voltage  when  the  cell  is  delivering  10  amperes  is  only  2  volts, 
what  is  the  internal  resistance  of  the  cell  ? 

5.  A  battery  of  24  lead  storage  cells  in  series,  each  having  an  e.m.f. 
of  2.1  volts,    a  normal   charging  rate  of  15  amperes,  and  an  internal 
resistance  of  0.005  ohms,  is  to  be  charged  by  a  dynamo,  what  must  be  the 
terminal  voltage  Of  the  dynamo  ? 


SUMMARY    OF   PRINCIPLES    IN    CHAPTER   XVIII 

When  a  wire  cuts  lines  of  force,  an  induced  e.m.f.  is  set  up 

in  the  wire. 

To  get  direction  of  current,  use  right  hand. 
Thumb  =  Motion, 
Forefinger  =  Flux, 

Center  finger  =  Direction  of  Current. 
Magnitude  of  e.  m.  f.  varies  as  speed  X  flux  X  turns. 

Slip  rings  give  alternating  current. 
Commutator  gives  direct  current. 


356  PRACTICAL  PHYSICS 

Dynamo  does  not  make   energy;   it  transforms  mechanical  into 

electrical  energy. 
Motor  transforms  electrical  energy  into  mechanical  energy. 

Power  delivered  to  circuit  =  intensity  of  current  X  voltage. 
Watts  =  amperes  X  volts. 
1  H.  P.  =  746  watts. 

Power  turned  into  heat  =  current  squared  X  resistance. 

Watts  =  (amperes)2  X  ohms. 
Heat  in  calories  =  0.24  I2Rt. 

A  wire  carrying  a  current,  when  set  at  right  angles  to  a  mag- 
netic field,  is  pushed  sideways  by  the  field. 

To  get  direction  of  motion,  use  left  hand.     As  before, 

Thumb  =  Motion, 

Forefinger  =  Flux, 

Center  finger  =  Current. 

Every  motor,  when  running,  is  acting  at  the  same  time  as  a 
dynamo.  The  e.m.f.  of  this  dynamo  action  opposes  the  current 
driving  the  motor,  and  is  the  back  e.  m.f. 

Net  e.m.f.,  which  drives  current  through  armature,  equals  im- 
pressed e.  m.  f.  minus  back  e.  m.  f . 

Ohm's  law  applies  to  a  motor  armature  only  if  net  e.  m.  f.  is 
used. 

Weight  of  a  substance  deposited  by  a  current 

=  electrochemical  equivalent  X  current  X  timec 

QUESTIONS 

1.  Why  cannot  a  lead  storage  cell  be  charged  from  a  dry  cell  ? 

2.  Why  do  the  lights  on  an  electric  car  often  grow  dim  when  the  car 
is  crowded  and  going  up  grade  ? 

3.  Would  it  be  possible  to  drive  the  propellers  of  an  ocean  liner  by 
electric  motors?     Why  is  it  not  commonly  done?     Why  are  some  people 
seriously  considering  doing  it  in  the  near  future? 


ELECTRIC  POWER  357 

4.  Which  will  yield  the  more  heat  for  warming  an  electric  car,  a  50 
ohm  resistance  connected  across  a  50  volt  line,  or  a  100  ohm  resistance 
connected  across  a  100  volt  line  ? 

5.  Compare  the  cost  per  hour  of  running  a  55  ohm  electric  heater  on 
a  55  volt  circuit  and  on  a  110  volt  circuit,  if  power  costs  10  cents  per 
kilowatt  hour. 

6.  The  "carrying  capacity"  of  a  wire  is  limited  by  the  rate  at  which 
it  can  radiate  the  heat  generated  in  it.     Which  will    require  wires  of 
larger  carrying  capacity,  a  1100  volt  power  transmission  line,  carrying 
1000  amperes,  or  a  11,000  volt  line,  carrying  100  amperes? 

7.  Which  of  the  lines  in  the  last  problem  will  deliver  more  power  at 
the  other  end  ? 

8.  Why  are  electric  cars  not  more  generally  operated  on  storage  cells 
instead  of  by  an  overhead  or  a  third-rail  system  of  transmission  ? 

9.  Why  are  electric  light  bills  made  out  in  kilowatt  hours  instead  of 
kilowatts  ? 

10.  Why  does  it  take  twice  as  much  power  to  keep  a  generator  going 
when  there  are  200  incandescent  lamps  lighted  in  parallel  as  when  there 
are  only  100  lamps  in  use? 

11.  What  methods  are  used  to  make  the  track  of  a  street-car  system 
a  better  conductor  ? 

12.  If  you  were  to  charge  a  storage  battery  so  incased  that  you  could 
see  only  the  two  terminals  which  were  marked  +  and  — ,  how  would 
you  connect  it  to  a  generator  ? 

13.  How  does  the  back  e.  m.  f .  of  a  motor  vary  with  its  speed  ? 

14.  A  belt-driven  shunt  dynamo  is  used  to  charge  a  storage  battery. 
The  belt  breaks,  but  the  dynamo  keeps  on  running.     Explain. 

15.  Does  it  make  any  difference  which  end  of  the  field  coils  of  a 
shunt-wound   dynamo  is  connected  with  the  positive  brush  ?      If  you 
have  an  experimental  dynamo,  try  it. 

16.  The  speed  of  a  shunt-wound  motor  can  be  controlled  by  putting 
an  auxiliary  resistance,  called  a  field  rheostat,  in  series  with  its  field  coils, 
so  as  to  decrease  the  current  through  them.     Will  this  increase  or  de- 
crease its  speed?     Why?    If  you  have  an  experimental  motor,  try  it. 

17.  What  is  the  advantage  of   electrotype  plates  over  the  original 
type  in  printing  a  book  ? 


CHAPTER    XIX 

ALTERNATING   CURRENT   MACHINES 

Why  alternating  currents  are  used  —  the  transformer  —  long- 
distance transmission  —  eddy  currents —  alternators  —  polyphase 
circuits  —  A.  C.  motors  —  rotating  field  —  squirrel-cage  rotor  — 
A.  C.  power  —  wattmeters. 

357.  Why  alternating  currents  are  used.  For  heating  and 
lighting  an  alternating  current  is  just  as  satisfactory  as  a 
direct  current.  For  plating  and  refining  an  alternating  cur- 
rent cannot  be  used  because  a  unidirectional  current  is  neces- 
sary to  make  a  metal  deposit.  If  motors  are  to  be  run  by  an 
alternating  current,  a  special  type  of  motor  is  generally  used, 
which  is  quite  different  from  the  ordinary  direct-current 
motor.  The  real  advantage  in  the  use  of  alternating  currents 

is  economy  of  transmission.  This  is 
made  possible  by  a  simple  and 
efficient  machine  known  as  a 
transformer. 

358.  Induced  currents  in  a 
transformer.  As  long  ago  as 
1831  Faraday  wound  two  coils 
of  wire  on  a  soft  iron  ring,  as 

FIG.  319.  —  Faraday's  ring  trans-        ,  .      ~  0^  ~        TTT1  ., 

former,  shown  in  figure  319.     When  coil 

A  was  connected  with  a  battery 

and  coil  B  with  a  galvanometer,  he  found  that  the  needle  of 
the  galvanometer  was  disturbed  every  time  the  circuit  was 
made  and  every  time  it  was  broken. 

The  modern  transformer  consists  of  two  coils  side  by  side  on 
a  common  iron  core  not  unlike  Faraday's  ring.     When  an 

358 


ALTERNATING   CURRENT  MACHINES 


359 


alternating  current  is  set  up  in  one  coil,  called  the  primary, 
it  magnetizes  the  iron  core,  causing  surges  of  magnetic  flux, 
first  in  one  direction  and  then  in  the  opposite  direction. 
Since  this  magnetic  flux  passes  through  the  second  coil,  called 
the  secondary,  as  well  as  the  first,  it  induces  an  alternating 
current  in  the  secondary.  Since  the  same  number  of  lines 
of  force  pass  through  both  coils,  the  volts  per  turn  are  the 
same.  Therefore  the  total  voltage  in  the  primary  coil  is  to  the~±<* 
total  voltage  in  the  secondary  coil  as  the  number  of  turns  in 
the  primary  is  to  the  number  of  turns  in  the  secondary. 

The  line  voltage  in  the  street  is  often  2200  volts,  which  is  too  high  to 

be  safely  used  in  private  houses.     It  is  therefore  necessary  to  transform 

or  "  step  down  "  to  110  volts.     A  primary  coil  of 

fine  wire  is  connected  to  the  2200  volt  circuit,  and 

a  secondary  coil  of  coarse  wire  is  connected  with 

the  lamp  circuit  of  the  house.  The  primary  coil 
must  have  20  times  as 
many  turns  as  the  sec- 
ondary. The  secondary 
coil  must  be  made  of 
larger  wire  than  the 
primary  coil,  because  the 
secondary  current  is 
about  twenty  times  the 
current  taken  by  the 
primary.  Thus  the  trans- 
former delivers  the  same 
amount  of  energy  which 
it  receives,  except  for  a 

small  amount  (from  2  %  to  5  %),  which  is  lost 
as  heat  in  the  transformer.  The  efficiency  of 
a  transformer  is  therefore  very  high,  from 
95  %  to  98  %. 

359.    Commercial    forms    of     trans- 
FIG.  321.  —Shell  type  of      former.     Transformers  are  built  in  two 

transformer.  -,   ,  ,   N    ,-,  ^^^. 

general  types  :   (a)  the  core  type  (tig. 

320),  in  which  the  coils  are  wound  around  two  sides  of  a 
rectangular  iron  core,  and  (5)  the  shell  type  (Fig.  321),  in 


FIG.  320.  —  Core  type 
of  transformer. 


360 


PRACTICAL  PHYSICS 


FIG.  322.  —  Transformer  case 
mounted  on  pole. 


which  the  iron  core  is  built  around  the  coils.     The  iron  core 
of  both  types  is  made  of  sheets  of  mild  steel.     To  keep  the 

coils  insulated,  the  transformer  is 
put  in  an  iron  case  and  surrounded 
with  oil.  These  iron  cases  (Fig. 
322)  are  commonly  attached  to  poles 
near  houses  wherever  the  alternat- 
ing current  is  used  for  lighting 
purposes. 

360.  Uses  of  transformers.  In 
electric  light  stations  it  is  common 
practice  to  use  alternators  to  gener- 
ate electricity  at  2200  volts.  The 
current  is  transmitted  at  this  high 
voltage  to  the  various  districts, 
where  it  is  transformed  or  "  stepped 
down"  to  110  volts  for  use  in  light- 
ing houses.  Another  important  use 
of  the  transformer  is  to  furnish  large  currents  at  very  low 
voltage  for  electric  furnaces  and  electric  welding. 

To  illustrate  this,  we  may  wind  a  turn  or  two  of  very  large  copper 
wire  around  the  core  of  a  small  step-down  transformer  (Fig.  323),  and 
connect  its  primary  to  a  110  volt  A.C. 
circuit  (if  one  is  available).  The 
ends  of  the  large  wire  should  be  at- 
tached to  a  couple  of  iron  nails.  If, 
when  the  current  is  on,  the  tips  of 
the  nails  are  brought  together,  they 
get  red  hot  and  can  be  welded. 

The  adjoining  rails  of  a  car 
track  are  often  welded  together 
in  this  way.  A  heavy  current 
is  required  for  a  short  time, 
and  is  obtained  by  using  a  step- 
down  transformer,  in  which  the  secondary  consists  of  only 
one  or  two  turns,  made  of  very  large  copper  bars.  The  ends 


FIG.  323.  —  Step-down  transformer, 
used  for  welding. 


ALTERNATING   CURRENT  MACHINES  361 

of  this  secondary  are  clamped  to  the  rails  to  be  welded,  one 
on  each  side  of  the  junction. 

381.  Long  distance  transmission  of  power.  By  the  use  of 
alternating  currents  of  high  voltage,  even  up  to  100,000 
volts,  power  is  now  transmitted  very  long  distances.  For 
example,  electric  power  is  generated  in  hydroelectric  power 
plants  in  the  Sierra  Nevada  Mountains  of  California,  and 
transmitted  200  miles  to  San  Francisco.  To  understand 
why  the  economical  transmission  of  electricity  demands 
such  high  voltage,  we  have  only  to  recall  that  the  power 
transmitted  is  the  product  of  the  voltage  and  the  current 
strength.  Evidently,  then,  if  we  can  make  the  voltage  high, 
the  current  can  be  low.  But  a  smaller  current  means 
smaller  losses  in  transmission,  for  they  are  due  to  the  heat- 
ing effect  of  the  electric  current,  and  we  have  already  seen 
that  this  varies  as  the  square  of  the  current. 

It  is  an  impressive  sight  to  see  three  or  six  copper  cables, 
each  about  |  of  an  inch  in  diameter,  suspended  about  75  feet 
above  the  ground  on  steel  towers  (Fig.  324,  opposite  page 
347),  and  to  know  that  those  wires  are  carrying  30,000  H.  P. 
of  electrical  energy.  Hydroelectric  power  plants  are  being 
developed  all  over  the  country.  For  example,  at  Niagara 
power  plants  are  generating  electricity,  raising  the  voltage 
to  60,000  and  transmitting  some  of  the  enormous  energy 
available  at  the  Falls  to  distant  cities  like  Buffalo,  Rochester, 
and  Syracuse.  Just  outside  the  city  limits  there  are  sub- 
stations where  the  voltage  is  reduced  to  about  2000,  and 
then  it  is  distributed  to  factories  and  for  general  use  in 
lighting  and  traction.  Before  the  current  actually  enters 
the  buildings,  the  voltage  is  again  stepped  down  to  220  or 
110  volts. 

362.  Eddy  currents.  We  have  seen  that  the  cores  of 
transformers  are  made  of  soft  sheet-iron,  or  "  mild  steel," 
stamped  out  in  the  desired  shape  and  then  assembled.  In 
the  construction  of  induction  coils  the  cores  are  made  of 


862 


PRACTICAL   PHYSICS 


Insulation 

FIG.  325.  — Laminated  core  of 
a  dynamo  armature. 


soft  iron  wires  which  are  put  together  in  a  bundle.  If  we 
examine  the  armature  of  a  dynamo,  we  find  that  the  iron 
drum  is  made  of  laminae  (sheets)  of  mild  steel  which  are 

stamped  out  in  the  shape  of  disks  with 
notches  around  the  edge  (Fig.  325), 
and  then  assembled  on  a  framework 
called  the  "  spider,"  and  mounted  on 
the  shaft.  .In  all  these  cases  the 
sheets  or  wires  are  insulated  from 
each  other  by  a  coating  of  shellac, 
which  eliminates  what  are  sometimes 
called  Foucault  or  eddy  currents. 
We  have  already  seen,  in  studying  the  generator,  that 
when  any  conductor  cuts  lines  of  force,  an  induced  electro- 
motive force  tends  to  send  a  current  along  the  conductor. 
In  the  generator  copper  wires  are  provided  to  carry  this 
current;  but  these  wires  are  wound  on  an  iron  core,  and  if 
this  core  is  itself  an  electrical  conductor,  an  induced  e.  m.  f. 
will  be  set  up  in  it  as  it  revolves  in  the  magnetic  field. 
This  induced  e.  m.  f.  would  send  electric  currents  through 
certain  portions  of  the  core.  These  so- 
called  eddy  currents  would  soon  heat 
the  core,  and  would  also  retard  the  mo- 
tion of  the  armature  and  waste  power. 
To  reduce  these  currents  to  as  small  a 
value  as  possible,  the  core  is  laminated 
in  such  a  way  that  the  insulation  is 
transverse  to  the  direction  in  which  the 
eddy  currents  tend  to  flow. 


363.  Use  of  eddy  currents  in  damping. 

To  show  that  eddy  currents  tend  to  retard  the 
motion  of  a  conductor  in  a  magnetic  field,  we  may 
set  up  between  the  poles  of  a  strong  electro- 
magnet a  pendulum  made  of  thick  sheet  copper  (Fig.  326).     If  the  mag- 
net is  not  excited,  the  pendulum  swings  back  and  forth  as  any  pendulum 


FIG.  326.  — Damping  by 
eddy  currents. 


ALTERNATING   CURRENT  MACHINES  363 

does,  but  when  we  throw  on  the  current  in  the  magnet,  the  copper  pendu- 
lum cannot  swing  through  the  magnetic  field,  and  is  instantly  checked. 
The  eddy  currents  set  up  in  the  copper  tend  to  retard  the  motion  of  the 
pendulum,  much  as  if  "it  were  swinging  in  thick  sirup. 

This  effect  is  very  useful  in  stopping  the  vibrations  of  the 
moving  coil  of  a  d'Arsonval  galvanometer  (section  274). 
The  wire  is  usually  wound  on  a  light  copper  or  aluminum 
frame,  and  the  eddy  currents  in  this  metal  frame  check  its 
swinging.  Such  a  galvanometer  is  called  "dead-beat."  We 
shall  see,  in  section  372,  that  this  same  principle  is  used  to 
check  the  rotation  of  a  wattmeter. 

QUESTIONS  AND  PROBLEMS 

1.  What  limits  the  voltage  which  it  is  practicable  to  use  on  high- 
tension  transmission  lines? 

2.  Why  are  the  cables  for  long-distance  transmission  sometimes  made 
of  aluminum  instead  of  copper? 

3.  If  a  step-down  transformer  is  to  be  used  to  change  the  voltage 
from  1100  to  220,  what  must  be  the  ratio  of  turns  of  wire  on  the  primary 
and  secondary  coils? 

4.  A  transformer  has  1000  turns  on  the  primary  and  50  turns  on  the 
secondary  and  the  primary  current  is  20  amperes.     About  how  much  is 
the  secondary  current? 

5.  What  generates  the  heat  required  to  weld  the  nails  in  the  experi- 
ment shown  in  figure  323  ?     Why  does  not  the  copper  wire  S  melt  as 
well  as  the  the  tips  of  the  nails? 

364.  Alternators.  When  a  coil  of  wire  is  rotated  in  a 
magnetic  field,  we  have  seen  (section  319)  that  the  current 
changes  its  direction  every  half  turn.  That  is,  there  are  two 
alternations  for  each  revolution  in  a  bipolar  machine.  In  a 
D.  C.  generator  this  alternating  current  is  rectified  by  the  use 
of  a  commutator.  In  the  alternating  current  (A.  C.)  gener- 
ator, called  an  alternator,  the  current  induced  in  the  armature 
is  led  out  through  slip  rings,  or  collecting  rings,  as  shown 
in  figure  275.  So  almost  any  direct-current  generator  can  be 
made  into  an  alternator  by  substituting  slip  rings  for  the 
commutator. 


364 


PRACTICAL   PHYSICS 


The  field  magnet  of  an  alternator  is  usually  an  electro- 
magnet which  is  excited  by  direct  current  from  a  small 
auxiliary  generator  called  the  exciter. 

Since  it  is  only  the  relative  motion  of  the  armature  wind- 
ings and  field  magnet  which  is  essential  in  any  generator, 

large  alternators  are  usually 
built  with  a  stationary  arma- 
ture and  a  revolving  field.  The 
revolving  projecting  poles 
(JV,  8,  N,  8,  in  figure  327) 
sweep  past  the  armature 
wires  which  are  placed  in 
slots  around  the  inner  pe- 
riphery of  the  stationary 
structure  A.  The  direct 
V  current  for  exciting  the 
field  coils  is  led  in  through 

FIG.  327. — Revolving  field  and  stationary    ,          ,  ,  .    ,  , 

armature.  brushes  which  rub  on   two 

insulated  metal  rings.     The 

alternating  current  is  led  directly  from  the  windings  of  the 
stationary  armature  through  cables  to  the  switchboard. 
Figures  328,  329,  and  330  (opposite  pages  364  and  365)  show 
the  revolving  field  and  stationary  armature  of  commercial 
machines  of  this  type,  and  an  assembled  machine. 

365.  Cycles  and 
phase  of  alternating 
currents.  When  a 
conductor  is  moved 
past  a  magnetic  N- 
pole,  the  induced 
e.  m.  f.  is  in  one  di- 
rection, and  when  it 


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FIG.  331.  —  Alternating  e.  m.  f.  one  complete  cycle. 


moves  past  an  $-pole,  the  induced  e.  m.  f.  is  in  the  opposite 
direction.  This  can  be  best  represented  by  the  curved  line 
shown  in  figure  331.  One  complete  wave  is  produced  when 


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FIG.  329  (above).  —  Stationary  armature  of  alternator. 

FIG.  330  (below).  —  Alternator,  belt  driven.  The  long  shaft  allows  the  arma- 
ture to  be  slid  to  one  side  so  that  the  rotor  can  be  examined  and  repaired. 
The  small  "exciter  "  is  on  the  end  of  the  shaft  at  the  right. 


ALTERNATING   CURRENT  MACHINES 


365 


a  wire  moves  through  a  complete  revolution  in  a  bipolar 
machine,  or  from  a  north  pole  past  a  south  pole  to  the  next 
north  pole  in  a  multipolar  machine,  and  is  called  a  cycle. 

In  practice  it  is  common  to  use  for  lighting  an  alternating 
current  whose  frequency  is  60  cycles  per  second,  while  for 
power  purposes  25 
or  even 
currents 
mon. 

A  complete  wave 
or  cycle  is  called 
360  electrical  degrees 


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FIG.  332. — Two  alternating  currents  which  differ  in 
phase. 


by  analogy  with  the 
complete  revolution 
of  a  bipolar  generator.  Any  point  or  position  in  the  cycle  is 
spoken  of  as  a  certain  phase.  When,  for  example,  the  cycle 
is  half  completed,  the  phase  is  said  to  be  180  degrees,  and 
when  the  cycle  is  one  fourth  completed,  the  phase  is  90  de- 
grees. Two  alternating  currents  of  electricity,  flowing  in 

branch  circuits,  may  be 
at  different  phases,  as 
represented  in  figure 
332,  where  one  .curve 
represents  the  current  in 
one  branch  and  the  other 
curve  the  current  in  the 
other  branch.  In  the 
case  shown,  one  current 
is  said  to  lag  behind  the 
other  by  90  degrees. 

FIG.  333.  —  Diagram  to  represent  armature  and          0-_ 

field  coils  on  alternator.  ^OO-     Single  and  pOly- 

phase    circuits.     If   we 

connect  all  the  stationary  armature  coils  of  a  generator  in 
series,  and  revolve  the  field  as  shown  in  figure  333,  a  single- 
phase  alternating  current  is  produced  whose  frequency  we  can 


Circwf 


366 


PRACTICAL   PHYSICS 


determine  by  multiplying  the  number  of  revolutions  per  second 
of  the  rotor  by  the  number  of  pairs  of  poles.  To  make  use  of 
this  current  for  any  purpose,  such  as  electric  lighting,  we 
have  simply  to  cut  this  armature  circuit  at  any  convenient 


step-down 
transform 


2300  volts 


2300  volts 


2300  volts 


FIG.  334.  —  Alternating  system  three  phases  and  six  wires. 

point  and  connect  the  ends  directly  to  the  mains.  It  will  be 
noticed  that  there  are  as  many  coils  on  the  armature  as  there 
are  poles  in  the  field  magnet  in  the  single-phase  machine. 

It  has  been  found  more  economical  of  space  to  have  more 
than  one  coil  for  each  pole  of  the  field,  and  so  we  have 
two-phase  and  three-phase  machines,  in  which  there  are  two  or 
three  sets  of  coils  on  the  armature.  In  the  three-phase 

machine,  which  is  the  type 

T\  /$~\  /s~\  ^~\  /^\  /-"      most  used  to-day,  the  three 

sets  of  armature  coils  may 
2  each  be  used  separately  to 
furnish  electricity  for  three 
separate  lighting  circuits,  as 
shown  in  figure  334. 

FIG.  335. — Curves  for  three-phase  current         — ,,  .        .         , 

system.  The  currents  in  the  three 

circuits   differ  in   phase  by 

120  degrees  (Fig.  335).  It  will  be  seen  that  the  currents 
are  such  that  at  any  instant  their  sum  is  zero. 


ALTERNATING   CURRENT  MACHINES 


367 


To  save  wire,  electrical  engineers  have  devised  ways  of 
connecting  the  three  sets  of  coils  so  as  to  have  only  three- 
line  wires,  instead  of  six,  as  shown  in  figure  336. 

367.  Use  of  alternators.  The  revolving-armature  type  of 
alternator  is  generally  used  only  in  small  electric  lighting 
stations.  Large  alternators  of  the  re- 
volving-field type  are  usually  mounted 
on  the  same  shaft  (direct-connected) 
with  the  driving  engine  or  water 
wheel.  Alternators  of  very  large  ca- 
pacity are  now  extensively  used  with 
steam  turbines.  They  can  be  com- 
paratively small  in  size  because  they 
are  driven  at  such  high  speed.  These 
alternators  have  a  revolving  field  of 
only  a  few  poles  (sometimes  only  two) 
and  a  wide  air  gap  between  the  ar- 
mature core  and  the  field  poles.  Figu  re 
337  shows  a  7500  kilowatt  alternator 
mounted  on  the  crank  shaft  of  a  10,000 
horse-power  steam  turbine,  having  a 
speed  of  1800  revolutions  per  minute. 
In  high-tension  transmission,  the  three-wire  three-phase  sys- 
tem is  commonly  used. 


FIG.  336.  —  Y  and  A  con- 
nections on  three-phase  cir- 
cuit. 


QUESTIONS 

1.  How  can  the  engineer  at  the  power  house  control  the  frequency  of 
an  alternating  current? 

2.  How  many  revolutions  per  minute  will  an  8-pole  machine  have  to 
make  to  give  a  60-cycle  current  ? 

3.  What  objection  is  there  to  using  a  15-cycle  current  for  lighting 
purposes  ? 

4.  Draw  a  diagram  to  show  two  alternating  currents  which  differ  in 
phase  by  45  degrees. 

5.  How  much  do  the  two  currents  generated  by  a  two-phase  alternator 
differ  in  phase  ? 


368 


PRACTICAL  PHYSICS 


Line  If 


368.  Alternating  current  motors.     An  A.  C.  generator  can 
be  run  as  a  motor,  provided  it  is  first  brought  up  to  the  exact 
speed  of  the  alternator  which  is  supplying  current  to  it  and 
put  in  step   with  the  alternations  of  the  current  supplied. 
Such  a  machine  is  called  a  synchronous  motor.     Since  it  is  not 
self-starting,  it  is  not  convenient  for  general  use,  but  is  used 
in  substations  to  drive  D.  C.  generators. 

An  ordinary  series  motor,  by  certain  modifications  in  its 
design,  can  be  made  to  operate  on  either  D.  C.  or  A.  C. 
systems.  These  so-called  A.  C.  commutator  motors  or  single- 
phase  series  motors  are  coming  into  use  for  electric  cars  and 
locomotives  when  an  alternating  current  is  used.  They 

are  also  to  be  found,  in  very 
small  sizes,  on  egg-shaking 
machines  in  drug  stores, 
and  on  vacuum  cleaners. 
They  are  labeled  "  A.C.  or 
D.C."  on  the  name  plates. 
The  A.  C.  motor  most 
frequently  used  is  the  in- 
duction motor.  The  distinc- 
tive features  of  this  motor 

FIG.  338.  —  Iron  ring  excited  by  two  currents    are      that     the      stationary 

90  degrees  apart.  winding,  or  "  stator,"  sets 

up  a  rotating  magnetic  field,  and  that  the  rotating  part  of  the 
motor,  or  "rotor,"  is  built  on  the  plan  of  a  squirrel  cage.* 
These  will  be  discussed  in  turn. 

369.  Rotating  magnetic  field.     To  produce  a  rotating  field, 
we  will  suppose  that  we  have  two  alternating  currents  of 
the  same  frequency,  but  differing  in  phase  by  90  degrees,  and 
that  we  connect  them  to  two  sets  of  coils  wound  on  a  ring, 
as  shown  in  figure  338. 

When  the  current  in  line  I  is  at  a  maximum,  it  will  be  seen 
from  the  curves  (Fig.  339)  that  the  current  in  line  II  is 
zero.  The  top  of  the  ring  is  therefore  a  north  pole,  Nv  and 


ALTERNATING   CURRENT  MACHINES 


369 


the  bottom  is  a  south  pole,  S.  One  eighth  of  a  cycle  (45 
degrees)  later,  current  1  has  decreased  in  strength  and  cur- 
rent 2  has  increased  in  strength.  The  result  of  both  currents 
is  to  form  a  north  pole  in  the  position  Nv  45  degrees  farther 
along.  One  eighth  of  a  cycle  (45  degrees)  later,  current  I 
has  dropped  to  zero  and  current  II  is  at  a  maximum.  This 
brings  the  north 
pole  of  the  ring 
to  the  right  side 
(iV3).  Evidently 
the  north  pole  is 
traveling  around 
the  ring,  and  will 
make  a  complete 
circuit  for  each  complete  cycle  of  the  current.  This  produces 
a  rotating  field,  and  would  cause  a  magnet,  such  as  NS,  to  ro- 
tate with  the  field.  We  should  then  have  a  little  two-phase 
A.  C.  motor. 

Figure  340  shows  a  working  model  to  demonstrate  the  rotating  field 
produced  by  a  two-phase  current  system. 

370.    The  rotor  of  an  induction  motor.     The  rotating  mag- 
net can,  of  course,  be  replaced  by  an  electromagnet,  which 


FIG.  339.  —  Curves  of  two  alternating  currents,  which 
differ  in  phase  by  90  degrees. 


FIG.  340.  — Working  model  of  two-phase  rotating  field. 

is  excited  by  some  outside  source  of  direct  current.  The 
rotor  of  a  commercial  A.C.  motor  is,  however,  much  simpler, 
It  consists  of  an  iron  core,  much  like  the  core  of  a  drum 

2B 


370  PRACTICAL  PHYSICS 

armature,  with  large  copper  bars  placed  in  slots  around  the 
circumference  and  connected  at  both  ends  to  heavy  copper 
rings.  This  is  called  a  squirrel-cage  rotor  (Fig.  342). 

When  it  is  placed  in  a  rotating  magnetic  field,  the  con- 
ductors on  the  two  sides  and  the  rings  across  the  ends  act 
like  a  closed  loop  of  wire,  and  a  large  current  is  induced, 
even  though  the  rotor  has  no  electrical  connection  with  any 
outside  circuit.  This  large  induced  current  makes  a  magnet 
of  the  iron  core,  and  the  field,  acting  on  this  magnet,  drags 
it  around. 

The  rotor  can  never  spin  quite  as  fast  as  the  magnetic  field. 
If  it  did,  there  would  be  no  cutting  of  lines  of  force,  no  cur- 
rents would  be  induced,  and  there  would  be  no  power  avail- 
able to  drive  the  rotor  against  its  load. 

As  in  the  case  of  the  Gramme  ring  dynamo,  the  ring  wind- 
ing is  riot  used  in  practical  motors.  The  common  construc- 
tion is  to  slip  coils  into  slots  in  the  inner  periphery  of  a 
laminated  iron  "  stator,"  as  shown  in  figure  341.  A  squirrel- 
cage  rotor  (Fig.  342)  is  simple  and  strong,  and  needs  only  to 
be  kept  cool.  This  is  done  by  air  circulated  through  the 
core  by  fan  blades.  The  assembled  machine  (Fig.  343)  is 
simple,  strong,  compact,  and  almost  "fool-proof."  For  these 
reasons,  the  induction  motor  is  finding  a  wide  field  of  useful- 
ness in  shops  and  factories,  and  even  on  electric  locomotives. 

371.  A.  C.  power.  We  have  seen  that  we  can  determine 
the  power  of  a  direct-current  circuit  by  multiplying  the  volts 
and  amperes  together.  With  a  non-inductive  circuit,  such 
as  a  lamp,  we  can  do  the  same  with  alternating  currents. 
In  the  case  of  machines  which  have  self-induction,  that  is, 
coils  of  wire  with  iron  cores,  the  number  of  volt  amperes  is 
greater  than  the  true  number  of  watts.  Although  we  cannot 
attempt  to  show  in  this  book  just  how  the  watts  may  be 
computed  from  the  volts  and  amperes  of  an  alternating  cur- 
rent, yet  we  can  see  why  it  is  not  a  simple  case  of  multipli- 
cation. 


FIG.  337  —7500  k.w.  alternator  driven  by  steam  turbine. 


FIG.  341.  —  Stator  of  an  induction  motor. 


FIG.  342.  —  Squirrel-cage  rotor  of  induction  motor. 


FIG.  343.  —  Induction  motor. 


ALTERNATING   CURRENT  MACHINES  371 

In  the  first  place,  we  will  represent  the  varying  electro- 
motive force  by  the  "  pressure  "  curve  in  figure  344,  and  the 
varying  current  by  the  current  curve  in  the  same  figure.  It 
will  be  noticed  that  the  current  curve  lags,  that  is,  it  starts 
after  the  e.  m.  f.  curve.  This  is  due  to  the  self-induction  of 
the  circuit  which  impedes  the  flow  of  the  alternating  current. 
To  get  the  power  of  such  a  current,  we  should  have  to  mul- 
tiply the  simultaneous  values  of  current  and  pressure  for  a 
great  number  of  points,  and  then  get 
a  general  average  of  these  products. 

Now  what  an  A. C.  ammeter  (which 
we  will  not  attempt  to  describe)  re- 
cords, is  the  "  effective  value  "  of  the 
alternating  current ;  that  is,  the  value 
in  amperes  of  the  direct  current  which 
would  produce  the  same  heating  FIG.  344.— Voltage  and  cur- 
effect.  It  can  be  shown  that  this 

"  effective  value  "  of  an  alternating  current  is  about  0.7  of  its 
maximum  value.  The  effective  value  of  an  electromotive 
force  is  said  to  be  one  volt,  when  it  will  develop  an  alternat- 
ing current  of  one  ampere  in  a  non-inductive  resistance  of 
one  ohm.  It  is  also  about  0.7  of  the  maximum  value  of  the 
e.  m.  f.  Evidently  it  will  not  do  to  multiply  these  effective 
values  of  current  and  voltage  together,  because,  in  the  averag- 
ing process  described  above,  large  values  of  the  current  are 
likely  to  be  paired  with  small  values  of  the  e.  m.  f.,  and  vice 
versa. 

It  can  be  shown  that  the  A.  C.  watts  are  equal  to  the  volt- 
amperes  times  a  factor,  which  is  called  the  power  factor.  This 
factor  varies  according  to  the  circuit.  It  is  always  less  than 
1  for  an  inductive  circuit. 

372.  Wattmeters.  Every  user  of  electricity  should  be  in- 
terested in  the  recording  wattmeter,  which  records  on  dials,  like 
those  of  a  gas  meter,  the  number  of  kilowatt  hours  of  elec- 
tricity consumed.  It  is  on  the  readings  of  this  instrument. 


372 


PRACTICAL  PHYSICS 


that  the  monthly  bills  are  based.  Figure  345  shows  the 
Thomson  form  of  wattmeter.  It  is  really  a  little  shunt 
motor,  the  armature  of  which  turns  at  a  speed  proportional 
to  the  rate  at  which  electrical  energy  is  passing  through  it. 
This  armature  is  geared  to  the  recording  dials.  The  field  of 
the  instrument  is  made  by  stationary  field  coils  which  are 
connected  in  series  with  the  line.  The  field  strength  is 


Dials 


Brushes-one/ 


FIG.  345.  —  Thomson's  watt-hour  meter. 

therefore  proportional  to  the  current  flowing  in  the  main 
line.  The  armature  is  connected  across  the  line,  and  takes  a 
current  proportional  to  the  voltage  across  the  line.  There- 
fore, the  torque  which  turns  the  armature  is  proportional  to 
the  product  of  the  current  and  the  voltage ;  that  is,  to  the 
watts  in  the  line. 

The  inertia  of  such  a  machine  would  make  it  run  too  fast, 
or  fail  to  stop  when  the  current  stopped,  if  it  were  not  for  the 
electric  damping  caused  by  the  rotation  of  an  aluminum  disk 
between  the  poles  of  permanent  magnets.  The  eddy  cur- 
rents generated  in  the  disk  tend  to  retard  its  motion. 

This  type  of  wattmeter  is  used  for  both  A.  C.  and  D.  C. 
work.  When  used  with  alternating  currents  it  automatically 
averages  the  products  mentioned  at  the  top  of  page  371. 


ALTERNATING   CURRENT  MACHINES  373 

SUMMARY   OF  PRINCIPLES   IN   CHAPTER   XIX 

In  a  transformer :  — 

Voltage  on  primary          turns  of  primary 
Voltage  on  secondary      turns  of  secondary 

In  an  alternator :  — 

Frequency  =  revolutions  per  second  x  number  of  pairs  of  poles. 

A.  C.  power  =  amperes  x  volts  x  power  factor. 
Power  factor  usually  less  than  one. 

QUESTIONS 

1.  The  iron  case  of  a  transformer  is  often  corrugated.     Why? 

2.  Why  must  the  dielectric  strength  of  the  oil  used  in  transformers  be 
carefully  tested  ? 

3.  In  long-distance  transmission  of  power  by  high-tension  lines,  the 
wires  are  often  supported  on  steel  towers  50  feet  or  more  above  the 
ground,  and  the  company  gets  a  right  of  way  to  a  strip  of  land  100  feet 
wide  over  which  to  run  its  wires.     WThy  these  precautions  ? 

4.  What  is  gained  by  making  the  armature  of  big  alternators  station- 
ary, and  rotating  the  field? 


CHAPTER   XX 


SOUND 


What  makes  sound  —  what  carries  sound  —  velocity  of  sound 

—  water  waves  —  velocity,  wave  length,  and  frequency  —  longi- 
tudinal waves  —  sound  waves  —  loudness  and  distance  —  direct- 
ing sound  —  reflecting  sound  —  musical  tones  —  intensity,  pitch, 
and  quality — resonators-  — overtones — beats  —  the  musical  scale 

—  stringed    instruments  —  wind    instruments  —  membranes  — 
the  phonograph. 

373.  What  makes  sound  ?  When  a  bell  rings,  we  see  the 
hammer  or  clapper  hit  the  bell,  and  hear  the  sound  which  it 
makes.  If  we  hold  a  pencil  against  the  edge  of  the  bell  just 
after  it  has  been  struck,  we  find  that  the  metal  is  moving  to 
and  fro  very  rapidly.  When  a  guitar  string  is  plucked,  it 
gives  forth  a  note  which  we  can  hear,  and 
at  the  same  time  we  can  see  that  the  string 
looks  broader  than  when  at  rest.  We  con- 
clude that  the  string  is  vibrating  or  oscil- 
lating back  and  forth.  When  we  strike  a 
tuning  fork  and  hold  it  near  the  ear,  we 
hear  a  note,  and  if  we  touch  the  fork  to 
the  lips,  we  feel  its  vibratory  motion. 

To  make  visible  the  vibration  of  a  tuning  fork 
let  us  touch  it  to  a  light  glass  bubble  suspended  on 
a  thread  (Fig.  346).  The  bubble  is  set  violently 
in  motion. 

Another  way  to  show  the  vibratory  motion  of  a 
fork  is  to  attach  a  point  of  stiff  paper  to  one  prong. 
Let  us  set  such  a  fork  in  vibration  and  draw  it  over 
a  piece  of  smoked  glass  (Fig.  347).  The  curve  which  is  traced  is  easily 
made  visible  by  putting  white  paper  behind  the  glass. 

~  374 


FIG.  346.  —  Vibration 
of  tuning  fork  made 
visible. 


SOUND 


375 


Whenever  we  look  for  the  source  of  a  sound,  we  find  that 
something  has  been  set  in  motion.     It  may  be  that  something 
has  fallen,  a  bell  has  been 
struck,  a  whistle  has  been 
blown,   or   some   one  has 
shouted;    always   some- 
thing has  been  set  vibrat- 

,  .   ,     ,  3    ,  -,  FIG.  347.  —  Curve  traced  by  a  vibrating 

ing  which  has  caused  the  fork 

sensation  of  sound. 

374.  What  carries  sound?  Ordinarily  the  air$  which  is 
everywhere  about  us,  brings  sound  to  our  ears.  To  make 
this  evident  let  us  try  the  following  experiment. 

Let  us  suspend  an  electric  bell  under  the  receiver  of  a  good  vacuum 
pump,  as  shown  in  figure  348.  If  we  set  the  bell  to  ringing  and  then 
pump  out  the  air,  we  find  that  the  sounds  be- 
come fainter  and  fainter.  When  we  let  the 
air  in  again,  the  bell  sounds  as  loud  as  at  first. 
It  seems  probable  that  the  bell  would  become 
quite  inaudible  if  we  could  get  a  perfect  vacu- 
um, and  if  no  sound  were  conducted  out  by  the 
suspension  wires. 


We  know  that  both  heat  and  light 
can  traverse  a  vacuum,  as  in  the  case 
of  the  electric  incandescent  light  bulb, 
but  we  see  from  the  last  experiment 
that  sound  does  not  traverse  a  vacuum. 
It  can  be  shown  that  other  gases  be- 
sides air  carry  sound,  and  that  liquids 
and  solids  are  even  better  carriers  of 
sound  than  gases.  For  example,  if  one  holds  his  ear  under 
water  while  some  one  hits  two  stones  together  at  some  dis- 
tance away,  the  sound  is  heard  very  distinctly.  It  is  also  a 
familiar  fact  that  one  can  hear  a  train  a  long  distance  away 
by  putting  one's  ear  close  to  the  steel  rail.  Loud  sounds,  like 
those  of  cannon,  or  of  volcanic  eruptions,  can  be  heard  at  a 


FIG.  348.  —  Sound  is  not  car- 
ried through  a  vacuum. 


376  PEACTICAL  PHYSICS 

distance  of  several  hundred  miles  by  putting  one's  ear  to 
the  ground. 

To  show  that  liquids  transmit  sound,  let  us  put  the  stem  of  a  tuning 
fork  into  a  hole  bored  in  a  large  cork.  If  we  set  the  fork  in  vibration, 
it  is  hardly  audible;  but  if  we  hold  it  with  the  cork  resting  on  the  sur- 
face of  a  glass  of  water,  we  hear  it  distinctly.  The  sounds  seem  to  be 
coming  from  the  table  on  which  the  tumbler  of  water  stands.  This  ex- 
periment shows  that  the  vibration  of  the  tuning  fork  is  transmitted 
through  the  cork  and  the  water  to  the  air  in  the  room. 

To  show  that  solids  transmit  sound,  we  may  hold  one  end  of  a  long 
wooden  stick  against  a  door,  and  rest  a  vibrating  tuning  fork  on  the 
other  end ;  the  sound  of  the  fork  seems  to  be  coming  from  the  door. 
The  wooden  stick  here  serves  as  the  sound  carrier  and  transmits  the 
vibration  of  the  fork  to  the  door. 

So  we  conclude  that  solids,  liquids,  and  gases  may  serve 
as  carriers  of  sound. 

375.  How  fast  does  sound  travel  ?  In  an  ordinary  room  one 
is  not  aware  that  it  takes  any  appreciable  time  for  sound  to 
travel  from  its  source  to  one's  ears;  but  in  a  large  hall,  or  out 
doors,  one  often  hears  an  echo,  which  shows  that  sound  does 
take  time  to  travel  to  a  reflecting  surface  and  back.  During 
a  thunder  shower  we  hear  the  roll  of  the  thunder  after  we 
see  the  flash.  The  farther  away  the  lightning  discharge  is,  the 
longer  the  interval  between  seeing  the  flash  and  hearing  the 
rumble.  Every  one  has  doubtless  seen  the  steam  from  a  dis- 
tant whistle,  and  then  later  heard  the  whistle.  So  there  is 
no  doubt  that  sound  travels  much  more  slowly  than  light. 

One  way  to  measure  how  fast  sound  travels  is  to  discharge 
a  cannon  on  a  distant  hill  and  measure  the  time  between  see- 
ing the  flash  of  the  cannon  and  hearing  its  report.  In  one 
such  experiment,  which  was  performed  by  two  Dutch  scien- 
tists in  1823,  the  cannons  were  set  up  on  two  hills  about  eleven 
miles  apart,  and  observations  were  made  first  from  one  hill 
and  then  from  the  other,  to  eliminate  the  error  due  to  wind. 
They  concluded  that  sound  travels  1093  feet  (or  333  meters) 
per  second,  which  was  remarkably  near  the  truth,  considering 


SOUND  377 

the  instruments  they  had.  Since  then,  several  men  have 
made  determinations  of  the  velocity  of  sound  in  air,  which 
show  that  at  0°  C  and  76  centimeters  pressure  the  velocity 
of  sound  is  1087  feet  (  or  331  meters)  per  second.  The  speed 
of  sound  in  water  is  about  4.5  times  the  speed  in  air,  and  in 
steel  it  is  more  than  15  times  as  great  as  in  air.  It  has  also 
been  found  that  the  speed  of  sound  in  air  increases  about  2 
feet  (or  0.6  meters)  per  second  for  each  degree  centigrade 
rise  in  temperature.  For  practical  purposes  it  is  enough  to 
remember  that  sound  travels  about  1100  feet  per  second. 

PROBLEMS 

(Assume  that  the  time  taken  by,  light  to  travel  ordinary  distances  is  negligibly 

small) 

1.  The  sound  of  a  steam  whistle  is  heard  2.6  seconds  after  the  steam 
is  seen.     About  how  far  away  is  the  whistle  ? 

2.  A  man  can  see  the  hammer  strike  a  bell  once  every  2  seconds.     If 
the  man  is  a  mile  away,  w^hat  is  the  interval  between  the  sounds  of  each 
stroke  ? 

3.  On  a  hot  summer  day,  when  the  temperature  is  30°  C,  the  flash  of 
a  gun  is  seen  2  miles  away.     How  long  after  the  flash  will  the  report 
of  the  gun  be  heard  ? 

4.  A  stone  is  dropped  from  the  top  of  the  Woolworth  Building  in 
New  York,  which  is  750  feet  high.     How  long  before  a  man  on  top 
would  hear  the  sound  of  the  stone  as  it  struck  the  pavement?     (The 
time  includes  the  time  for  the  stone  to  fall  and  for  the  sound  to  return.) 

5.  If  an  experiment  shows  that  sound  travels  in  water  4814  feet  per 
second  at  14°  C,  how  many  times  as  fast  does  sound  travel  in  water  as  in 
air  at  this  temperature  ? 

376.  Sensation  of  sound.  We  have  been  considering  the 
transmission  of  "  sound  "  through  gases,  liquids,  and  solids, 
although  we  know  that  it  is  merely  a  sort  of  motion  which 
is  transmitted.  Ordinarily  we  find  it  hard  to  think  of 
sound  without  thinking  of  an  ear  to  hear  it.  Thus  we  find 
people  asking  whether  a  waterfall  in  a  very  remote  part  of 
the  earth,  never  visited  by  any  man  or  animal,  makes  any 


378  PRACTICAL   PHYSICS 

sound.  Evidently  there  are  two  things  which  are  called 
"  sound  "  the  vibrations,  and  the  sensation  they  produce  when 
they  strike  against  the  tympanum  or  eardrum.  The  study 
of  what  happens  in  the  ear  and  brain  is  properly  left  to 
physiology  and  psychology.  In  physics  we  shall  study  only 
the  vibrations  in  the  air  or  other  transmitting  medium,  and 
shall  refer  to  them  when  we  say  "sound."  In  this  sense  the 
waterfall  makes  just  as  much  sound  whether  there  is  an  ear 
to  hear  it  or  not. 

377.  Sound  a  wave  motion.     Evidently  nothing  material 
(that  is,  weighable)  travels  from  the  source  of  a  sound  to  the 
ear;  otherwise,  how  did  the  sound  of  the  electric  bell  under 
the  bell  jar  get  through  the  glass  ?     This  and  other  facts  point 
unmistakably  to  the  conclusion  that  what  is  transmitted  is 
merely  a  vibration  or  mode  of  motion,  called  a  wave. 

378.  Water  waves.     Since  sound  waves  are  usually  invisi- 
ble, we  will  start  with  a  study  of  water  waves.     When  a  stone 
is  dropped  into  a  smooth  pond,   a  disturbance  is  produced 
which  extends  over  the  surface  of  the  water  in  circles  centered 
at  the  place  where  the  stone  struck.     The  water  is  pushed 
down  and  aside  by  the  stone,  forming  a  circular  ridge  which 
expands  into  a  larger  circle,  and  is  followed  by  a  second  cir- 
cular ridge  which  expands,  and  so  on.     The  result  is  that  the 
surface  is  soon  covered  with  a  series  of  circular  swells  which 
are  separated  by  circular  troughs,  all  moving  away  from  the 
center  of  the  disturbance. 

To  study  these  water  waves  more  carefully,  let  us  pour  water  into  a 
long  tank  with  glass  sides  (Fig.  349)  to  a  depth  of  2  inches,  set  a  paddle 
upright  about  6  inches  from  one  end  of  the  tank,  and  start  a  wave  by 
drawing  the  paddle  to  the  end  of  the  tank.  It  will  be  observed  that  the 
wave  travels  to  the  other  end  of  the  tank.  There  it  is  turned  back  or 
reflected,  returning  to  the  first  end,  undergoing  another  reflection,  and  so 
on.  By  measuring  the  length  of  the  tank  and  observing  the  time  of  six 
round  trips  of  a  wave  (observe  the  rise  and  fall  of  the  water  at  one  side) 
we  can  calculate  the  speed  of  the  wave. 

If  we  pour  more  water  into  the  tank  until  the  depth  is  3  inches,  and 


SOUND  379 

again  time  six  round  trips  and  calculate  the  speed  of  the  wave  motion, 
we  shall  find  that  waves  travel  faster  in  deep  water. 

To  study  stationary  water  waves  we  place  a  little  block  on  the  water 
at  one  end  of  the  tank.     By  raising  and  lowering  the  block  periodically, 


FIG.  349.  —  Tank  for  water  waves. 

we  may  set  up  stationary  water  waves,  in  which  the  water  simply  "  see- 
saws "  up  and  down  with  no  apparent  backward  and  forward  motion. 

The  surface  of  a  water  wave  may  be  represented  by  the 
curved  line  shown  in  figure  350.  The  stationary  points, 
A,  -B,  (7,  .Z),  etc.,  are  called  the  nodes ;  the  intervening  spaces 
are  called  the  loops,  or  internodes.  The  water  between  nodes 
oscillates  up  and  down;  when  it  is  up,  it  forms  a  crest,  and 
when  it  is  down,  it  is  a  trough.  A  crest  and  trough  together 
form  a  wave,  as  from  A  to  C,  or  B  to  D. 

The  length  of  a  wave  (0  is  measured  K — ? — 1 

^X^v9       cs~^P  2J~"-P^- 
horizontally   from   any  point   on   one 

wave  to  the  corresponding  point  in  the 

,  P  J  FIG.  350.  —  Surface  of  a 

next  wave.     Corresponding  points  are  water  wave< 

called  points  in  the  same  phase.     The 

amplitude  (d)  of  the  wave  vibration  is  half  the  vertical  dis- 
tance from  trough  to  crest. 

379.  Relation  between  velocity,  wave  length,  and  frequency. 
In  the  case  of  the  waves  started  by  throwing  a  stone  into  a 
quiet  pool,  we  know  that  while  the  circular  waves  grow 
larger  and  larger,  any  particular  crest  seems  to  move  out 
radially  until  it  reaches  the  bank  or  dies  away.  The  dis- 
tance which  a  crest  travels  in  one  second  is  called  its  velocity. 
The  number  of  crests  passing  a  fixed  point  in  one  second  is 
called  the  frequency.  The  time  it  takes  one  wave  to  pass  a 


380  PRACTICAL  PHYSIQS 

given  point,  that  is,  the  time  between  crests,  is  called  the 
period  of  the  wave  motion. 

If  n  is  the  number  of  waves  passing  a  given  point  in  one 
second,  that  is,  the  frequency,  and  if  p  is  the  time  required  for 
one  wave  to  pass  a  given  point,  that  is,  the  period,  then, 


Again,  if  I  is  the  length  of  one  wave  in  feet,  and  n  is  the 
number  of  waves  passing  any  point  in  one  second,  the  dis- 
tance traveled  by  a  wave  in  one  second,  that  is,  its  velocity  v 
in  feet  per  second,  is  equal  to  n  times  I  ;  that  is, 

v  =  nl 

It  should  be  remembered  that  it  is  only  the  wave  form  that 
travels  over  the  surface  of  the  water,  not  the  water  particles 
themselves.  Thus  if  we  float  a  cork  or  a  toy  boat  ou  a  pool 
over  whose  surface  waves  are  passing,  the  cork  or  boat 
merely  bobs  up  and  down  as  a  wave  passes,  but  is  not  carried 
along  with  it. 

380.  Transverse  and  longitudinal  waves.  An  easy  way  of  illus- 
trating wave  motion  is  to  fasten  one  end  of  a  piece  of  rubber  tubing  about 

20  feet  long  to  a  hook 

jmr^^*  ^^^^  ^-^    in  the  wall.     If  we 

(11(10)  -  ^       ^^^^  ^Gl    take  the  free  end  in 

FIG.  351.  —  Waves  in  a  rubber  tube.  the  hand,  we  can,  by 

a  quick  shake,  send 

a  wave  along  the  tube  (Fig.  351).  If  a  single  depression  is  sent  along 
the  tube  to  the  fixed  end,  it  is  reflected  and  returns  as  an  elevation  ;  in 
like  manner  a  single  elevation  sent  along  the  tube  comes  back  as  a  de- 
pression. 

In  the  case  of  water  waves  and  of  the  waves  in  a  tube  or 
cord,  the  particles  of  water  or  tubing  oscillate  up  and  down, 
while  the  disturbance  moves  horizontally.  Such  waves  are 
called  transverse  waves. 

A  second  kind  of  wave  motion  takes  place  in  substances 
such  as  gases  and  wire  springs,  which  are  elastic  and  com- 


SOUND 


381 


pressible.  This  kind  of  wave  can  be  studied  by  letting  a 
coil  of  wire  represent  the  substance  through  which  such  waves 
are  transmitted. 

Figure  352  represents  a  spring  whose  turns  are  large  and  are  supported 
by  threads.  If  we  strike  the  spring  at  one  end,  we  compress  a  few  turns 
near  that  end.  These  move  slightly  and  compress  those  just  ahead,  and 


WOK 

FIG.  352.  —  Spring  wave  model. 

these  in  turn  squeeze  together  the  turns  still   farther   along.     Thus  a 
pulse  or  wave  goes  along  the  spring. 

Next  let  one  end  of  the  spring  be  given  a  quick  pull,  so  that  the  turns 
near  by  are  drawn  apart  for  an  instant.  Then  the  adjacent  turns  will  be 
pulled  over,  one  after  another,  until  this  disturbance  reaches  the  other 
end.  Thus  it  is  seen  that  any  push  or  pull  given  to  the  spring  at  one 
end  is  transmitted  as  a  push  or  pull  to  the  other  end. 

Waves  of  this  sort,  in  which  the  particles  of  the  transmit- 
ting material  move  back  and  forth  in  the  direction  of  the 
advance  of  the  wave,  are  called  compression  or  longitudinal 
waves. 

381.  Longitudinal  vibration  in  solids.  Not  only  springs, 
but  gases  and  even  solids  like  steel,  transmit  vibrations  longi- 
tudinally. 

If  we  clamp  a  steel  rod  in  the  middle  and  rub  it  lengthwise  with  a 
cloth  dusted  with  rosin,  a  clear,  ringing  sound  may  be  produced.  That 
the  rod  has  been  set  in  vibration  longitudinally  can  be  shown  by  a  little 


382 


PRACTICAL   PHYSICS 


FIG.  353.  —  Ball  driven  from  end  of  rod. 


ivory  ball  hung  by  a  cord  so  as  to  rest  against  the  end  of  the  rod.    When  the 
rod  is  vibrating,  the  ball  will  swing  violently  out,  as  shown  in  figure  353. 

Another  mechanical  illustration  of  the  method  by  which  a 
push  or  pull  may  travel  a  long  distance,  although  the  individ- 
ual particles  move 
only  very  minute 
distances,  is  shown 
in  the  following  ex- 
periment :  — 

The  apparatus  shown 
in  figure  354  consists  of 
several  glass-hard  steel 
balls  hung  up  in  a  line 
so  that  they  just  touch 
each  other.  If  we  pull 
aside  the  first  ball  and 

let  it  fly  back  and  strike  the  line  of  balls,  the  ball  it  strikes  does  not 

seem  to  move,  nor  the  next  one.     In  fact  none  seem  to  be  affected  by  the 

blow  except  the  ball  on  the  opposite 

end,  which  flies  out  about  as  far  as 

the  first  ball  fell. 

Since  steel  is  very  elastic, 
the  impact  of  the  first  ball  is 
handed  along  from  ball  to 
ball  until  it  reaches  the  end 
one.  It  is  as  though  a  push 
were  given  to  the  first  of  a 
column  of  boys  standing  in 
line.  It  is  transmitted  along 
the  line,  and  the  last  boy  is 
pushed  over. 

382.  Sound  waves.  We 
think  of  the  air  in  sound 
waves  as  vibrating  to  and  fro  in  the  direction  of  propagation 
like  the  turns  of  the  spring ;  that  is,  sound  waves  are  longi- 
tudinal or  compression  waves,  made  up  of  alternate  condensations 


FIG.  354.  —  Illustrating  how  sound  travels 
from  particle  to  particle. 


SOUND 


383 


rarefactions.  Just  as  a  stone  thrown  into  a  pool  makes 
waves  which  spread  out  in  ever  widening  concentric  circles, 
so  we  think  of  a  bell  as  sending  out  spherical  waves.  These  are 
made  up  of  alternate  spherical  shells  of  compressed  and  rare- 
fied air,  traveling  out  in  every  direction  through  space. 

To  form  a  picture  of  a  sound  wave  traveling  through  a 
speaking  tube,  let  us  imagine  that  the  spiral  spring  of  the 
model  (Fig.  352)  is  replaced  by  a  column  of  air,  which  has  a 


A  n 

ffftffWtf^ 


FIG.  355.  —  Diagram  to  show  sound  waves  by  a  curve. 

tuning  fork  at  one  end,  giving  little  pulses  to  the  air  column, 
while  an  eardrum  at  the  other  end  receives  these  pulses 
(Fig.  355). 

The  successive  condensations  and  rarefactions  of  the  air 
are  indicated  by  c  and  r  iii  A.  The  disturbance  travels  from 
the  fork  to  the  air,  but  the  intervening  air  at  any  point 
merely  oscillates  a  very  little  to  and  fro.  The  curve  in 
figure  355  is  a  graphical  representation  of  these  sound 
waves,  in  which  the  crests,  1-2,3-4,  etc.,  represent  conden- 
sations or  compressions,  and  the  troughs,  2-3,  etc.,  represent 
rarefactions.  The  amplitude  of  the  wave  corresponds  to  the 
distance  each  particle  of  air  moves  to  and  fro  from  its  origi- 
nal position.  A  sound  wave  includes  a  complete  crest  and 
trough,  that  is,  a  condensation  and  rarefaction,  and  the  dis- 
tance between  two  corresponding  points  in  any  two  adjacent 
waves  is  called  the  wave  length. 


384  PRACTICAL  PHYSICS 

Since  the  same  relation  between  velocity,  wave  length,  and 
frequency  holds  for  sound  waves  as  for  water  waves,  we  can 
easily  compute  the  length  of  a  sound  wave. 

Suppose  a  tuning  fork  is  giving  256  vibrations  each  second,  and  that 
the  velocity  of  sound  is  1120  feet  per  second.  Then  the  length  of  each 
wave  is  1120  feet  divided  by  256,  or  about  4.4  feet. 

Or  substituting  in  the  wave  equation, 

v=  nl, 

1120  =  256  I, 
1  =  4.4  feet. 

To  picture  a  sound  wave  spreading  through  the  open  air, 
we  may  imagine  a  great  number  of  spiral  springs  radiating 
out  from  a  common  center  at  the  source  of  the  sound,  all  re- 
ceiving an  impulse  at  the  same  time. 

PROBLEMS 

1.  An  A  tuning  fork  on  the  "  international  scale  "  makes  435  vibra- 
tions per  second.     What  is  the  length  of  the  sound  wave  given  out? 

2.  A  vibrating  string  gives  out  sound  waves  2  feet  long.     What  is  the 
frequency  of  the  waves? 

3.  The  period  of  a  sound  wave  is  found  to  be  0.0025  seconds.     What 
is  the  length  of  the  wave  ? 

4.  A  bell  whose  frequency  is  150  vibrations  per  second  is  sounded 
under  water,  in  which  sound  travels  at  the  rate  of  4800  feet  per  second. 
Find  the  wave  length  produced  by  the  bell. 

5.  If  the  highest  tone  which  the  ear  can  recognize  makes  80,000  vi- 
brations per  second,  what  is  the  shortest  w-ave  which  the  ear  appreciates? 

•383.  Intensity  or  loudness  of  sound.  It  must  always  be  re- 
membered that  when  a  bell  is  struck,  the  sound  is  heard  in  all 
directions,  which  means  that  sound  waves  spread  out  in  all 
directions  as  shown  in  figure  356.  As  the  distance  from  the 
source  increases,  the  spherical  waves  spread  out  over  more 
surface,  and  so  the  intensity  of  the  sound  decreases.  For 
example,  a  bell  10  feet  away  will  sound  one  fourth  as  loud 
as  the  same  bell  5  feet  away,  and  if  15  feet  away,  it  sounds 


SOUND  385 

one  ninth  as  loud  as  when  5  feet  away.  This  is  because  the 
energy  of  the  wave  must  be  imparted  to  nine  times  as  many 
particles  at  a  distance  of  15  feet  as  at  a  distance  of  5  feet. 
In  general,  the  intensity  of  sound  varies  inversely  as  the  square 
of  the  distance. 

If  one  ascends  to  a  high  altitude,  as  on  a  mountain  top  or 
in  a  balloon  or  aeroplane,  the  air  becomes  less  dense  and  so 
not  so  good  a  carrier  of  sound. 
This  makes  it  difficult  to  transmit 
sounds.     In  general,  the  intensity 
of  sound  depends  on  the  density  of 
the  medium  through  which  the  sound 
is  transmitted. 

384.  Speaking  tubes  and  mega- 
phones.    The  speaking  tubes  used  to 
connect  rooms  in  buildings   and 
ships  serve  to  prevent  the  spread- 
ing out  of  sound  waves  in  all  di- 
rections, and  SO  the  SOUnd  is  heard     FIG.  356.  —  Sound  waves   spread 
with  almost  its  original  intensity       °0u^a11  directions  from  this 
at  the  distant  point.     Sharp  bends 

in  such  tubes  should  be  avoided,  as  they  cause  reflected  waves, 
which  run  back. 

In  the  megaphone  the  sound  waves  which  come  from  the 
mouth  are  not  permitted  by  the  walls  of  the  instrument  to 
spread  out  in  all  directions.  In  this  way  the  energy  of  the 
voice  is  sent  largely  in  one  direction. 

385.  Reflection  of  sound.     Just  as  any  elastic  body  like  a 
rubber  ball  bounds  back  when  thrown  against  a  brick  wall, 
or  a  water  wave  is  turned  back  by  a  stone  enbankment,  so  a 
sound  wave  is  turned  back  or  reflected  when  it  strikes  against 
another  body,  such  as  a  building,  cliff,  or  wooded  hillside,  or 
even  a  cloud.     The  returning  wave  is  called  an  echo.     If  the 
reflecting  wall  is  near,  as  in  a  closed  room,  one  may  hear  an 
echo  almost  at  the  same  instant  as  the  sound.     This  confuses 

2c 


386 


PRACTICAL   PHYSICS 


a  hearer,  and  is  an  acoustical  defect  in  the  room.  It  can  often 
be  remedied  by  putting  an  absorbing  material  on  the  reflect- 
ing wall.  When  the  reflecting  surface  is  25  or  more  yards  dis- 
tant, the  echo  is  distinct  from  the  original  sound,  and  excites 

interest  and  curiosity.  The 
greater  the  distance,  the  longer 
is  the  time  before  the  reflected 
wave  strikes  the  ear,  and  there- 
fore the  more  distinct  the  echo 
becomes.  When  we  have  par- 
allel walls,  as  in  a  narrow  canon, 
or  objects  at  different  distances, 
the  echo  is  multiple  or  repeated, 
which  means  that  the  same 
sound  is  heard  several  times. 
For  example,  the  roll  of  thunder 
results  in  part  from  the  reflection  of  the  sound  from  a  suc- 
cession of  mountains  or  clouds. 

The  following  experiment  shows  that  sound  waves,  like  light  waves, 
are  reflected  by  curved  surfaces.  If  two  large  parabolic  mirrors  face 
each  other,  as  in  figure  357,  a  watch  at  the  principal  focus  of  one  mirror 
can  be  distinctly  heard 
across  the  room  by  hold- 
ing an  ear  trumpet  at 
the  focus  of  the  other  " 


FIG.  357.  —  Sound  of  a  watch  reflected 
by  mirrors. 


mirror. 


B 


FIG.  358.  —  Curves  to  represent  (A)  noise  and  (B) 
music. 


In  buildings  with 
arched  ceilings  it  is 
sometimes  possible 
to  hear  a  whisper  at  a  ver}^  distant  place  in  the  room  because 
the  sound  is  reflected  from  the  ceiling  and  concentrated  at 
the  ear  of  the  listener. 

386.  Musical  sounds  and  noises.  We  all  recognize  some 
sounds,  such  as  the  slamming  of  a  door  or  the  rumbling  of  a 
wagon  over  cobblestones,  as  noises;  while  we  recognize  the 


SOUND  387 

sounds  from  a  piano  wire  or  an  organ  pipe  as  musical  sounds 
or  tones.  The  difference  between  these  kinds  of  sounds  can 
be  best  expressed  by  the  curves  in  figure  358,  where  A  is 
the  curve  of  a  noise,  and  B  the  curve  of  a  musical  note. 

It  will  be  seen  from  these  curves  that  a  noise  makes  a  very 
irregular  and  haphazard  curve,  while  a  musical  note  makes 
a  uniform  and  regular  curve.  The  latter  produces  an  agree- 
able sensation  on  the  ear,  while  the  former  makes  a  disa- 
greeable sensation.  The  great  German  scientist,  Helmholtz, 
expressed  this  distinction  by  saying,  "  The  sensation  of  a 
musical  tone  is  due  to  a  rapid  periodic  motion  of  a  sounding 
body;  the  sensation  of  a  noise  to  a  non-periodic  motion." 

387.  Three  characteristics  of  a  musical  note.     A  musical 
sound  or  tone  has  intensity  or  loudness,  pitch,  and  quality  or 
timbre,  and  each  of  these  characteristics  depends  upon  some 
physical  property  of  the  sound   wave.     The  intensity   of   a 
sound  depends  on  the  amplitude  of  the  vibration;  the  pitch 
depends  on  the  frequency  of  the  waves;  and  the  quality  de- 
pends on  the  vibration  form. 

388.  Intensity.     We  have  already  seen  that  the  intensity 
of  sound  in  general  diminishes  as  the  distance  of  the    ear 
from  the  source  of  the  sound  increases  and  also  as  the  density 
of  the  air  diminishes.      The  intensity  of  a  musical  sound  for 
a  given  ear  and  at  a  given  distance  depends  on  the  amplitude 
of  vibration  of  the    waves   sent   out.     For  example,  a    piano 
string  or  a  tuning  fork  gives  a  louder  sound  when  struck 
hard  than  when  struck  gently. 

389.  Pitch.      When  we  speak  of  a  musical  note  as  high  or 
low,  we  refer  to  its  pitch.     When  we  strike  the  keys  of  a 
piano  in  succession,  beginning  at  one  end  of  the  keyboard,  we 
recognize  the  difference  in  the  tones  produced  as  a  difference 
in  pitch.     By  holding  a  card  against  the  teeth  of  a  rapidly 
revolving  wheel  (Fig.  359)  we  can  show  that  the  pitch  of  the 
note  produced  depends  on  the  number  of  vibrations  per  second; 
that  is,  upon  the  frequency  of  the  vibrations. 


388 


PRACTICAL  PHYSICS 


We  can  show  this  very  clearly  by  means  of  a  siren.  This  is  a  metal 
disk  (Fig.  360)  with  holes  equally  spaced  around  the  edge,  which  can 
be  rotated  by  some  sort  of  whirling  apparatus. 
If  a  current  of  air  is  directed  through  a  tube 
against  the  holes,  the  regular  succession  of 
puffs  produces  a  musical  tone.  As  we  in- 
crease the  velocity  of  the  wheel,  the  tone  be- 
comes higher ;  that  is,  its  pitch  is  raised. 

One  way  to  measure  the  frequency 
of  vibration  of  a  musical  tone  is  by 
FIG.  359.  —The  pitch  varies  means  of  such  a  rotating  disk.  Sup- 
pose the  disk  has  80  holes,  and  is  at- 
tached to  a  motor  making  1800  revolutions  per  minute. 
Since  the  disk  makes  30  revolutions  per  second,  there  are 
30  x  80^=2400  puffs  per  second.  The  fre- 
quency of  the  tone  emitted  would  be  2400 
vibrations  per  second.  This  would  be  a 
rather  shrill  note.  A  standard  A  tuning 
fork  makes  only  435  vibrations  per  second. 

390.  Limits  of  audibility.     The  lowest 
tone  which  the  human  ear  can  recognize  as 
a  musical  tone  has  a  frequency  of  about 
16  vibrations  per  second.     If  the  sound 
has  a  frequency  above  a  certain  number, 
the  ear  does  not  recognize  it  at  all.     This 
upper  limit  of  audibility  varies  with  differ- 
ent people  from  20,000  to  40,000  vibrations 

per  second.     A  young  person  can  usually'  Fl<?-  360-  — Pitch  de- 

•i        /.       i  .    i  .      .  pends  upon  the  rate 

recognize  sounds  of  a  higher  pitch  than  an      Of  vibration. 

older  person.     In  fact  this  is  one  of  the 

evidences  of  the  impairment  of  hearing  with  advancing  age. 

391.  Quality   or   timbre.     The   third    characteristic   of    a 
musical  note  is  its  quality.     It  is    quality  which  enables   us 
to  distinguish  between  notes  of  the  same  pitch  and  inten- 
sity as  produced  by  different  instruments  or  sung  by  differ- 
ent voices.     Even  the  same  kind  of  instrument  may  produce 


HERMANN  VON  HELMHOLTZ.  Born  near  Berlin,  in  1821.  Died  in  1894.  Trained 
as  a  physician  and  physiologist,  he  made  important  discoveries  in  mechanics, 
sound,  and  light,  as  well  as  in  mathematics  and  in  philosophy. 


SOUND 


389 


notes  of  different  quality.  For  example,  it  is  the  quality  of 
the  tones  produced  by  two  violins  which  makes  the  great 
difference  in  their  value.  We  recognize  the  voice  of  a  friend 
over  the  telephone  by  its  quality. 

Helmholtz  (1821-1894)  first  discovered  the  cause  of  these 
subtle  differences  in  musical  tones,  which  are  called  quality. 
In  this  investigation  he  made  use  of  resonators  which  vibrated 
in  sympathy  with  the  tones  to  be  studied. 

392.  Sympathetic  vibrations.  Every  one  has  learned  by 
experience  how  easy  it  is  to  set  a  swing  vibrating  by  a  suc- 


FIG.  361.  —  Sympathetic  vibration  of  forks  of  the  same  pitch. 

cession  of  gentle  pushes  applied  at  just  the  right  time,  so 
that  each  push  helps  rather  than  hinders  the  swinging. 
Mere  random  pushes,  on  the  other  hand,  accomplish  very 
little.  In  much  the  same  way  sound  waves  or  other  slight 
impulses  may  set  up  strong  vibrations  in  a  body  if  they  are 
timed  to  correspond  exactly  to  its  natural  frequency  of 
vibration.  This  is  called  sympathetic  vibration. 

It  can  be  strikingly  shown  by  holding  down  the  loud  pedal  of  a  piano, 
so  that  the  dampers  are  lifted  from  the  strings,  and  singing  a  clear,  strong 
tone  into  the  instrument.  After  the  voice  is  silent,  the  sound  is  returned 
by  the  strings  with  enough  fidelity  to  make  the  effect  almost  startling. 

Another  way  to  illustrate  sympathetic  vibrations  is  to  put  two  tuning 
forks  of  the  same  pitch  several  feet  apart  (Fig.  361).  If  we  strike  one 
fork  vigorously  with  a  soft  mallet,  and  then  quickly  stop  it  with  the  hand, 
the  other  will  be  heard  even  in  a  large  room.  It  has  been  set  in  motion 


390 


PRACTICAL   PHYSICS 


by  the  sound  waves  from  the  first  fork.  If  we  change  the  pitch  oi 
one  fork  by  sticking  a  bit  of  beeswax  on  one  prong,  the  forks  will  be 
thrown  slightly  out  of  unison  and  will  no  longer  respond  to  each  other. 

From  this  experiment  it  is  evident  that  two  tuning  forks 

must  vibrate  at  exactly  the  same  rate  to  vibrate  in  sympathy. 

Certain  articles  of  furniture  and  of  glassware  have  definite 
rates  erf  vibration  of  their  own,  arid  are 
set  vibrating  sympathetically  when  their 
particular  note  is  sounded.  It  is  the 
cumulative  effect  of  feeble  impulses  re- 
peated many  times  at  regular  intervals 
which  sets  up  this  sympathetic  vibration. 
393.  Resonators.  That  property  of  a 
sounding  body  which  enables  it  to  take 
up  the  vibrations  of  another  body  by 
sympathy,  and  to  vibrate  in  unison  with 
it,  is  called  resonance.  In  the  last  experi- 
ment each  tuning  fork  stood  on  a  wood 
box  open  at  one  end  and  so  constructed 
that  the  air  column  within  the  box  has 
the  same  rate  of  vibration  as  the  fork 

itself.     Such  an  air  column  is  called  a  resonator.     It  was  the 

resonator  rather  than  the  fork  itself  that 

picked  up  the  vibrations. 


FIG.  302.  —  Re  enforce- 
ment of  a  sound  by  an 
air  column. 


To  show  resonance,  we  may  raise  and  lower  the 
tube  A  (Fig.  362)  in  the  jar  of  water  B,  and  at 
the  same  time  hold  a  vibrating  tuning  fork  over 
the  tube.  We  shall  find  a  position  where  the 
sound  of  the  fork  is  reenforced  by  the  sound 
of  the  air  column  and  seems  loudest. 

This  reenforcement  or  intensification 
of  sound  by  a  resonator  is  due  to  the  uni- 
son of  direct  and  reflected  waves.  For 
example,  it  can  be  shown  that  the 
length  of  air  column  used  in  the  ex- 


FIG.  363. —The  cause 
of  resonance 


SOUND  891 

periment  is  one  quarter  of  a  wave  length.  This  will  be 
readily  understood  from  the  diagram  (Fig.  363),  where 
ac  is  one  prong  of  a  fork  vibrating  over  an  air  column  in 
resonance.  When  the  prong  moves  down  past  its  central 
position,  it  causes  a  condensation  in  the  column  of  air,  which 
goes  to  the  bottom  and  gets  back  just  as  the  fork  is  moving 
up  past  its  central  position.  This  reenforces  the  vibration 
of  the  fork.  Since  the  sound  traveled  twice  the  length  of 
the  air  column  in  the  time  of  half  a  vibration  of  the  fork,  it 
traveled  the  length  of  the  air  column  in  the  time  of  a  quarter 
vibration.  So  the  vibrating  air  column  is  a  quarter  of  a 
wave  length.  Further  experiments  would  show  that  a 
resonance  column  may  be  3,  5,  7,  or  any  odd  number  of 
quarter  wave  lengths. 

394.  Fundamentals  and  overtones.     When  a  piano  wire  vi- 
brates as  a  whole,  it  gives  out  what  is  called  its  fundamental 
note.     This  fundamental  is  the  lowest  note  which  it  can  give 
out.     Its  pitch  depends  on  the 

length,   tension,  size,  and  ma- 

terial  of  the  wire.  When  a  FIG.  364.  —  A  wire  emitting  its  funda- 
Wire  is  Vibrating  as  a  whole,  mental  and  first  overtone. 

it  may  at  the  same  time  be  vibrating  in  segments;  that  is,  as 
if  it  were  divided  in  the  middle.  Such  a  secondary  vibration 
gives  an  overtone  which  has  twice  the  frequency  of  the  funda- 
mental and  is  said  to  be  an  octave  higher.  Figure  364  shows 
an  instantaneous  picture  of  a  vibrating  string  giving  both  its 
fundamental  and  its  first  overtone.  In  a  similar  way,  a  string 
may  vibrate  as  a  whole  and,  at  the  same  time,  as  if  divided 
into  thirds,  in  which  case  it  gives  its  fundamental  and  its 
second  overtone.  Higher  overtones  or  "harmonics"  are 
also  possible. 

395.  Helmholtz'  experiment.     Helmholtz  proved  that  the 
quality  of  a  tone  is  determined  simply  by  the  number  and 
prominence  of  the  overtones  which  are  blended  with  the 
fundamental.     To  prove  this,  he  constructed  a  large  number 


392 


PRACTICAL  PHYSICS 


of  spherical  resonators  (Fig.  365),  each  having  a  large  open- 
ing, and  also  a  small  one  adapted  to  the  ear.  A  resonator 
of  this  form  is  especially  useful  because  it  responds  easily  to 
vibrations  of  one  pitch  only,  and  so  can 
be  used  to  analyze  sounds.  By  holding 
each  of  these  resonators  in  succession  to 
his  ear,  he  was  able  to  pick  out  the  con- 
stituents of  any  musical  note  which  was 
being  sounded,  and  to  judge  of  their 
relative  intensities.  Then  he  reversed 
the  process  and  combined  these  constit- 
uent overtones,  reproducing  the  original 
tone.  He  succeeded  in  imitating  in  this  way  the  qualities 
of  different  musical  instruments  and  even  of  various  vowel 
sounds. 

396.   Koenig's    manometric    flames.     Another   method   of 
showing  that  the  quality  of  any  note  depends  on  the  form  of 


FIG.  365.  —  Helmholtz' 
resonator. 


FIG.  366.  —  Analysis  of  sounds  with  manometric  flames. 


SOUND 


393 


the  wave  was  devised  by  a  Frenchman,  Koenig.  This  method, 
called  manometric  flames,  has  the  advantage  of  making  the 
phenomenon  visible. 

The  apparatus  is  shown  in  figure  366.  The  essential  part 
is  a  small  box  divided  into  two  chambers  by  an  elastic 
diaphragm,  made  of  very  thin  sheet  rubber  or  goldbeater's 
skin.  The  cavity  on  one  side  is  connected  with  a  funnel, 
while  the  cavity  on  the  other 
side  has  two  openings,  one  for 
illuminating  gas  to  enter,  and 
the  other  connected  with  a  fine 
jet  where  the  gas  burns  in  a 
small  flame.  The  vibrations  of 
the  air  on  one  side  of  the  dia- 
phragm change  the  pressure  of 
the  gas  on  the  other  side,  and 
cause  the  flame  to  dance  up  and 
down.  When  such  a  flame  is 
viewed  in  a  rotating  mirror,  its  FlG"  367.  -  Forms  shown  by  mano- 

metric  flames. 

image  is  a  straight  band  of  light 

[Fig.  367  (top)]  if  the  flame  is  still,  and  a  serrated  band 
[Fig.  367  (lower  three  curves)]  when  sound  vibrations  are 
striking  against  the  diaphragm. 

Let  us  set  up  the  apparatus  as  shown  in  figure  366,  and  first  rotate 
the  mirror  when  no  note  is  sounded  before  the  funnel.  There  will  be 
no  fluctuations  in  the  flame  as  the  mirror  is  turned.  Next  let  a  mounted 
tuning  fork  be  sounded  in  front  of  the  mouthpiece.  Then  let  each  of 
the  vowels  be  spoken  into  the  funnel  with  the  same  pitch  and  loudness. 
The  ribbon  of  flame  seen  in  the  mirror  is  different  in  each  case. 

Manometric  flames  can  be  used  to  study  sound  vibrations 
of  such  high  frequency  that  they  are  quite  inaudible. 

PROBLEMS 


.UMIMU.U. 


1.   If  two  men  are  1000  feet  and  2500  feet  from  a  foghorn,  how  many 
times  as  loud  does  the  horn  sound  to  one  man  as  to  the  other? 


394  PRACTICAL   PHYSICS 

2.  Six  seconds  elapse  between  the  firing  of  a  gun  and  its  echo  from  a 
cliff.     If  the  temperature  is  15°  C,  how  far  away  is  the  cliff? 

3.  A  tuning  fork   is   reenforced  when  held  over  an  air  column  6.5 
inches  long.     What  is  the  wave  length  ? 

4.  A  tuning  fork,  whose  normal  frequency  is  435,  is  mounted  on  a 
wooden  box,  which  acts  as  a  resonator.      If  we  neglect  the  correction 
for  the  end,  how  long  must  the  box  be  ? 

5.  A  whistle  has  a  resonating  column  of  air  1.5  inches  long.     Find 
the  vibration  frequency  of  its  tone. 

397.  Interference  of  sounds.     We  have  seen  in  studying 
resonators  that  two  sound  waves  may  unite  so  as  to  reenforce 
each  other.     It  is  also  possible  to  make  two  sound  waves 
unite  so  as  to  interfere  with  or  destroy  each  other.     That  is, 
under  certain  conditions  the  union  of  two  sounds  can  produce 
silence.     This  is  the  cause  of  the  phenomenon  called  beats. 

If  we  place  two  mounted  tuning  forks  of  the  same  pitch  side  by  side, 
and  strike  the  forks  in  succession  with  a  soft  mallet,  we  hear  a  smooth, 
even  tone.  But  if  we  change  the  pitch  of  one  fork  by  attaching  a  slider 
to  one  prong,  and  repeat  the  experiment,  we  hear  a  throbbing  or  pulsat- 
ing sound.  The  throbs  are  called  beats.  They  are  due  to  the  alternate 
interference  and  reenforcement  of  the  sound. 

If  two  adjoining  notes  of  a  piano  or  organ  are  struck  at  the  same 
time,  beats  are  heard,  especially  if  the  notes  are  in  the  lower  part  of  the 
scale. 

Beats  are  made  use  of  when  it  is  desired  to  tune  two 
strings  or  forks  to  the  same  pitch.  The  forks  are  adjusted 
until  no  beats  are  heard. 

398.  Explanation  of   beats.       To   show   how   two   sound 
waves  can  combine  to  produce  no  sound,  let  A  in  figure  368 

represent  a  sound  wave, 
and  B  another  wave  of  ex- 
actly the  same  period,  but 
opposite  in  phase  ;  that  is, 
just  a  half  wave  length 
,  behind  the  first.  If  the 

FIG.  368.  —  Two  waves  of  same  period  but 

opposite  phase.  two  impulses,  which  would 


SOUND 


395 


generate  two  such  waves,  were  applied  to  the  air,  it  would 
not  suffer  any  disturbance  at  all.  This  is  interference  of 
sound  waves. 

If  two  waves  of  the  same  period,  A  and  B,  in  figure  369, 
are  in  phase  or  in  step, 
they  reenforce  each 
other,  and  produce  a 
sound  of  double  ampli- 
tude,  as  shown  by  the 
dotted  curve  C.  This 
is  reenforcement  of  sound 
waves. 

Finally,  if  two  waves  of  slightly  different  period  (J.  and  B, 
in  figure  370)  are  superposed,  there  will  be  reenforcement 
at  some  points  and  interference  at  other  points,  as  shown  in 
the  third  curve  C. 

Evidently,  if  the  waves  make  respectively  255  and  256  vibrations  per 
second,  there  will  be  one  reenforcement  and  one  interference  (that  is,  one 


FIG.  369.  —  Two  waves  in  step  result  in 
reenforcement. 


FIG.  370.  —  Curves  to  show  how  beats  are  produced. 

beat)  each  second.     In  general,  the  number  of  beats  per  second  is  equal  to 
the  difference  between  the  frequencies  of  the  waves. 

399.  Discord  and  beats.  Experiments  show  that  discord 
is  simply  a  matter  of  beats.  If  there  are  six  beats  or  less 
per  second,  the  result  is  unpleasant,  but  if  there  are  about 
thirty,  there  is  the  worst  possible  discord.  When  the  vi- 
bration numbers  differ  by  as  much  as  seventy,  as  do  the  notes 


396  PRACTICAL  PHYSICS 

C  and  E,  the  effect  is  harmonious.  If  two  musical  tones 
with  strong  overtones  are  to  be  harmonious,  it  is  essential 
that  there  shall  not  be  an  unpleasant  number  of  beats  between 
any  of  their  overtones.  This  is  the  reason  why  the  bells  of 
chimes  are  struck  in  succession,  not  simultaneously. 

400.  The  musical  scale.  So  far  we  have  been  studying 
the  behavior  of  a  single  train  of  waves  in  the  air,  and  the 
propagation  of  a  single  musical  tone  ;  now  we  will  consider 
some  of  the  fundamental  relations  between  musical  tones. 
That  is,  we  shall  seek  a  scientific  basis  of  music. 

When  we  wish  to  compare  two  musical  tones,  we  first  con- 
sider their  pitch;  that  is,  their  frequencies.  Notes  of  the 
same  frequency  are  said  to  be  in  unison.  When  two  notes 
have  frequencies  as  1  to  2,  the  relation  or  interval  is  called 
an  octave.  For  example,  a  note  whose  frequency  is  512  is 
one  octave  higher  than  another  whose  frequency  is  256 ;  and 
one  whose  frequency  is  128  is  an  octave  below  the  note  whose 
frequency  is  256. 

It  has  been  found  that  the  ear  recognizes  as  harmonious 
only  those  pairs  of  notes  whose  frequencies  are  proportional 
to  any  two  of  the  simple  numbers,  1,  2,  3,  4,  5,  and  6.  It  is 
still  more  remarkable  that  the  ear  of  man  has  for  centuries 
recognized  that  three  notes  are  harmonious  when  their  fre- 
quencies are  as  4  :  5  :  6.  This  combination  is  called  the  major 
triad.  Any  combination  or  rapid  succession  of  tones  not  char- 
acterized by  simple  frequency  ratios  produces  a  discord. 

The  major  scale  is  a  sequence  of  tones  so  related  that  the 
1st,  3d,  and  5th  form  a  major  triad ;  also  the  4th,  6th,  and 
8th  ;  and  also  the  5th,  7th,  and  9th  (or  octave  of  the  2d).  This 
is  shown  in  the  following  table,  where  the  tones  of  the  scale 
are  represented  by  the  letters  used  in  musical  notation. 

The  arrangement  of  the  notes  of  an  octave  on  the  key- 
board of  a  piano  is  shown  in  figure  371.  The  white  keys 
correspond  to  the  notes  of  an  octave,  the  black  keys  to  in- 
termediate notes,  used  in  forming  other  scales. 


SOUND 


397 


TABLE  OF  RELATIONS  BETWEEN  NOTES  OF  AN  OCTAVE 


c 

(do) 

T^ 

D 

(re) 

E 

(mi) 

F 

(fa) 

G 

(sol) 

A 

(la) 

B 

(si) 

c 
(do^ 

d 

(re) 

5 

6 

4 

5 

6 

4 

5 

6 

i 

1 

1 

t 

1 

f 

¥ 

2 

1 

Any  frequency  or  vibration  number  may  be  given  to  the 
first  note  C  of  the  octave  and  the  series  built  up  as  indicated. 
In  fact  several 
such  pitches  have 
been  in  common 
use  as  the  starting 
point.  The  so- 
called  international 
pitch,  which  is 
now  almost  ex- 


clusively 
takes  435 


used, 
vibra- 


Piano 
Keyboard 

c'T^Te' 

I 

3 

Treble  |~X 

ciff     \\f\\                                              n 

S3      i        i 

Cie/     Ivu/                             Q       O       y 

Absolute  pitch  ^—  Y 
on  international  &      ^       ^       >o       «o 
«caZe               «o      3       £«      2.      S2 

;                      1 
is       oo        *^ 

2     22      ^ 

FIG.  371.  —  Notes  of  an  octave  on  piano  keyboard. 

tions  for  middle  A  (second  space  on  the  treble  cleff),  and 
this  makes  middle  C  (the  lower  C  on  the  treble  cleff)  258.6. 
In  physical  laboratories  C  forks  usually  have  a  frequency  of 
256,  to  make  the  arithmetic  easier. 


MUSICAL  INSTRUMENTS 

401.  Piano.  We  are  all  familiar  with  the  piano,  or  at 
least  we  have  seen  its  keyboard,  which  usually  has  88  keys. 
When  we  open  the  case,  we  find  88  wires  of  various  lengths 
and  sizes.  Each  key  operates  a  little  hammer  which  strikes 
a  wire  and  thus  produces  a  note  of  definite  pitch.  We  may 


398  PRACTICAL  PHYSICS 

also  notice  that  the  notes  of  lower  pitch  are  produced  b^ 
long,  large  wires  and  the  notes  of  higher  pitch  by  short,  thin 
wires.  Perhaps  we  have  watched  a  piano  tuner  loosen  or 
tighten  a  wire  by  turning  with  a  wrench  a  pin  at  one  end. 

If  we  stretch  a  piece  of  steel  wire  along  the  table  and  set 
it  vibrating,  we  find  its  tone  is  very  weak  compared  to  the 
tone  of  a  piano.  This  is  because  the  piano  has  a  sounding 
board  directly  beneath  the  wires.  The  vibrations  of  the 
wires  are  transmitted  through  the  frame  to  this  large  thin 
board,  causing  it  to  vibrate  also.  The  board  then  sets  a 


FIG.  372.  —  A  sonometer. 

larger  quantity  of  air  in  vibration  than  the  string  could  af- 
fect alone,  and  produces  a  louder  tone. 

402.  Laws  of  vibrating  strings.  We  may  show  by  means  of  a  so- 
nometer (Fig.  372),  which  is  simply  a  metal  wire  stretched  across  a  long 
wooden  box,  that  the  pitch  or  frequency  of  a  wire  is  raised  by  tightening 
the  wire.  If  we  introduce  a  movable  bridge  or  fret,  the  pitch  is  raised. 
The  shorter  we  make  the  wire  or  string,  the  higher  is  the  pitch.  Finally 
we  may  show  that  a  larger  wire  of  the  same  length  and  under  the  same 
tension  gives  a  lower  note. 

Careful  experiments  of  this  sort  have  proved  the  following 
laws :  — 

(1)  The  vibration  frequency  varies  inversely  as  the  length  of 
the  vibrating  string.     For  example,  a  wire   under   constant 
tension  can  have  its  pitch  raised  an  octave  by  putting  the 
movable  bridge  in  the  middle. 

(2)  The  vibration  frequency  varies   directly  as  the  square 
root  of  the  tension.     For  example,  if  a  pull  of  4  pounds  on  a 


SOUND 


399 


string  gives  100  vibrations  per  second,  a  pull  of  16  pounds 
is  required  to  raise  the  pitch  an  octave,  or  produce  200 
vibrations  per  second. 

(3)  The  vibration  frequency  or  pitch  varies  inversely  as  the 
square  root  of  the  weight  per  unit  length  of  the  string.  For 
example,  the  wires  on  the  piano  which  give  the  low  notes 
are  wound  with  wire,  to  get  the  necessary  weight. 

403.  Other  stringed  instruments.     The  violin,  mandolin,  and 
guitar  have  sets  of  strings   tuned  to  give  certain  notes,  and 
wooden  bodies  to  reenforce  the  tones  of  the  strings.     These 
instruments  differ  from  the  piano  in  that  they  have  but  few 
strings,  and  in  that  their  strings  are  set  in  vibration  by  bow- 
ing or  picking  instead  of  by  striking  them 

with  a  hammer.  Each  string  is  made  to  give 
a  large  number  of  notes  by  pressing  on  it  at 
various  places  and  so  changing  its  length. 
The  particular  place  and  manner  in  which  the 
string  is  plucked  or  bowed  determines  the 
overtones  and  thus  the  quality  of  the  tone. 
In  this  way  the  violin  may  be  made  to  give 
tones  with  a  wide  range  not  only  of  pitch 
but  also  of  quality. 

404.  Wind    instruments.       The    simplest 
wind  instrument  is  the  organ  pipe.     Sometimes 
the  tube  is  open  at  the  upper  end  and  is  called 
an  open  pipe  [Fig.  373  (J.)];  at  other  times 
the  pipe  is  closed  at  the  upper  end  and  is 
called  a  closed  pipe  [Fig.  373  (.#)]. 

If  we  blow  an  open  pipe,  the  current  of  air  strikes  against  a  sharp 
edge  and  is  set  in  vibration.  The  tube  acts  as  a  resonator.  The  lowest 
note  which  such  a  pipe  gives  out  is  the  one  whose  wave  length  is  twice 
the  length  of  the  pipe.  This  note  is  called  its  fundamental.  If  we  close 
the  end  of  the  tube  with  the  hand,  thus  making  a  closed  pipe,  we  shall 
find  that  the  lowest  note  is  an  octave  lower,  or  one  whose  wave  length 
is  four  times  the  length  of  the  pipe.  This  is  called  the  fundamental 
note  of  the  closed  pipe. 


A  B 

FIG.  373.  —  Organ 
pipes:  (A)  open, 
and  (B)  closed. 


400  PRACTICAL  PHYSICS 

In  general,  then,  the  length  of  an  open  pipe  is  one  half  the 
wave  length  of  its  fundamental,  and  the  length  of  a  closed  pipe 
is  one  quarter  of  a  wave  length  of  its  fundamental. 

It  will  be  noticed  that  the  resonance  tube  in  the  experi- 
ment in  section  393  is  a  closed  pipe  upside  down,  the  tuning- 
fork  end  corresponding  to  the  lip  end  of  an  organ  pipe. 

When  air  is  blown  more  violently  into  an  organ  pipe, 
overtones  may  be  produced. 

The  flute,  clarinet,  cornet,  and  trombone  are  also  wind  instru- 
ments. In  the  first  two,  the  column  of  air  is  broken  up  by 
means  of  holes.  The  opening  of  a  hole  in  the  tube  is  equiva- 
lent to  cutting  the  tube  off  at  the  hole.  In  the  trombone 
the  length  of  the  air  column  can  be  varied  by  sliding  a  por- 
tion of  the  tube  in  and  out.  It  is  also  possible  to  vary  the 
notes  by  blowing  harder  and  so  getting  overtones. 

In  wind  instruments  of  the  bugle  or  cornet  type,  the  vibra- 
tion of  the  air  is  caused  by  the  vibrating  lips  of  the  musician. 

405.  Vibrating  membranes.  One  example  of  this  sort  of 
musical  instrument  is  the  drum.  Another  is  the  most  won- 
derful musical  instrument  of  all,  the  human  voice.  It  is  pro- 
duced by  the  vibration  of  a  pair  of  membranes  on  each  side 
of  the  throat,  called  the  vocal  cords,  and  also  by  the  vibration 
of  the  tongue  and  lips.  By  changing  the  muscular  tension 
on  the  vocal  cords  one  changes  the  pitch  of  his  voice,  and  by 
changing  the  shape  of  the  mouth,  one  changes  the  overtones, 
and  so  the  quality  of  tone. 

PROBLEMS 

1.  An  open  pipe  is  4  feet  long.     What  wave  length  does  it  give? 

2.  What  is  the  length  of  an  open  pipe  which  gives  a  tone  an  octave 
above  that  in  problem  1  ? 

3.  A  siren  has  50  holes.     How  many  revolutions  per  minute  will  it 
have  to  make  to  produce  a  tone  whose  frequency  is  435  ? 

4.  A  fork  making  256  vibrations  per  second  is  reenforced  by  a  tube 
of  hydrogen  4  feet  long.     What  is  the  velocity  of  sound  in  hydrogen? 


SOUND 


401 


5.  Find  the  number  of  vibrations  of  a  note  three  octaves  below  a 
note  whose  frequency  is  264. 

6.  What  is  the  fourth  overtone  of  a  string  whose  fundamental  tone 
has  a  frequency  of  256  ? 

7.  The  keyboard  of  a  piano  has  7  octaves  and  2  notes.     If  the  lowest 
note  is  A4  (27),  what  is  the  frequency  of  the  highest  note  c""  ? 

8.  How  long  would  an  open  organ  pipe  need  to  be  to  give  the  note 
middle  A  (international  pitch)  ? 

9.  How  many  centimeters  long  would  the  closed  pipe  of  a  whistle 
need  to  be  to  give  middle  C  (international  pitch)  ? 

406.    The  phonograph.     The  phonograph  (Fig.  374),  which 
was  invented  by  Thomas  Edison,  is  a  remarkable  machine 


FIG.  374.  —  Cylinder   form  of  phonograph  and  diaphragm  with  recording  and 
reproducing  points. 

for  reproducing  sound,  especially  music  and  speech.  When 
the  instrument  is  recording  sound,  the  waves  set  a  diaphragm 
vibrating,  and  this  makes  a  fine  metal  or. sapphire  point, 
which  can  move  up  and  down,  cut  a  spiral  groove  of  varying 
depth  in  a  wax  cylinder.  The  bottom  of  this  groove  is  a 
wavy  line  representing  the  condensations  and  rarefactions  of 
the  sound  waves. 

To  reproduce  the  sound  a  small  round-ended  needle  is  at- 
tached to  the  diaphragm  and  follows  the  groove  in  the  wax 
as  the  cylinder  turns.  The  varying  depth  of  the  groove 
moves  the  needle  up  and  down  and  thus  makes  the  diaphragm 

2D 


402  PRACTICAL   PHYSICS 

vibrate  in  such  a  way  as  to  reproduce  the  original  sounds. 
In  the  machine  shown  in  figure  374,  the  sharp  and  the  round- 
ended  points  are  both  mounted  near  the  center  of  the  same 
diaphragm,  as  shown  at  the  right.  The  diaphragm  can  be 
moved  forward  and  back  a  little  so  that  only  one  of  these 
points  touches  the  cylinder  at  any  time. 

In  another  style  of  phonograph  (Fig.   375)    the   wax   is 
made  in  the  form  of  a  disk  instead  of  a  cylinder,  and  the 


FIG.  375.  —  Disk  form  of  phonograph  and  diaphragm. 

needle  point  vibrates  from  side  to  side  instead  of  up  and 
down. 

A  phonograph  does  not  reproduce  the  consonant  sounds 
very  distinctly,  words  being  chiefly  recognized  by  the  vowel 
sounds  which  come  out  strong  and  clear.  This  is  because 
the  vowel  sounds  are  more  or  less  clearly  defined  musical 
tones,  and  produce  regular  vibrations,  but  the  consonant 
sounds  are  noises  produced  by  the  mouth  at  the  beginning 
arid  end  of  vowel  sounds. 

SUMMARY   OF  PRINCIPLES   IN   CHAPTER   XX 

Sound,  in  physics,  is  a  vibratory  motion  transmitted  through  air 

or  other  gases,  liquids,  or  solids. 
Velocity  of  sound  is  about  1100  feet  per  second. 


SOUND  403 

(Accurately  it  is  1087  ft./sec.  at  0°  C,  and  it  increases  about  2 

ft./sec.  for  each  degree  C  rise.) 
Wave  length  =  distance  from  crest  to  crest  (or  from  condensation 

to  condensation). 

Frequency  =  number  of  waves  passing  given  point  in  one  second. 
Velocity  =  frequency  x  wave  length. 
Intensity  or  loudness  depends  on  amplitude. 
Pitch  (of  musical  tone)  depends  on  frequency. 
Quality  (of  musical  tone)  depends  on  wave  form ;  i.e.  on  number 

and  prominence  of  overtones. 
Pitch  of   a  string  (1)  Rises  when  length  is  decreased, 

(2)  Rises  when  tension  is  increased, 

(3)  Is  higher  for  small,  light  strings. 
Length  of  open  pipe  =  i  wave  length  of  fundamental. 
Length  of  closed  pipe  =  1  wave  length  of  fundamental. 

QUESTIONS 

1.  How  can  the  pitch  of  the  sound  from  a  phonograph  be  raised  ? 

2.  What  causes  a  difference  in  the  pitch  of  an  organ  pipe  between  a 
hot  day  in  summer  and  a  cold  day  in  winter  ? 

3.  How  can  a  bugler  produce  notes  of  varying  pitch  on  an  instru- 
ment of  unchanging  length  ? 

4.  Why  is  it  better  to  bow  a  violin  string  near  one  end  rather  than 
in  the  middle  ? 

5.  Is  any  difference  in  the  quality  of  a  violin  tone  noticeable  when 
tne  bow  is  moved  nearer  the  finger  board  ?     Why  ? 

6.  How  does  the  piano  tuner  go  to  work  to  tune  a  piano? 

7.  A  distant  band  sounds  much  the  same,  except  for  loudness,  as  a 
band  near  by.     What  does  this  indicate  about  the  velocity  of  sounds  of 
different  wave  lengths  ? 

8.  When  an  electric  light  bulb  breaks,  there  is  a  loud  crash.     Ex- 
plain. 

9.  A  man  has  two  open  organ   pipes  just  alike.     He   saws  off  a 
little  from  the  end  of  one.     Explain  what  is  heard  when  they  are  both 
sounded  together. 

10.    How  do  the  valves  on  a  cornet  operate  to  produce  the  different 
notes  ? 


404  PEACTICAL  PHYSICS 

11.  There  is  an  old  saying  that  "if  you  can  count  three  between  a 
flash  of  lightning  and  its  thunder  clap,  the  storm  is  not  dangerously 
near."     According  to  this  how  far  away  must  the  thunder  cloud  be  for 
safety  ? 

12.  Explain  just  why  the  resonance  experiment  described  in  section 
393  will  not  work  if  the  length  of  the  air  column  is  half  a  wave  length. 

13.  Explain  how  sound  is  produced  by  some  form  of  automobile  horn 
or  signal  in  common  use. 


CHAPTER   XXI 

LIGHT:    LAMPS   AND   REFLECTORS 

Illumination  —  law    of    inverse    squares  —  standard    lamps 
and  "  candle  power  "  —  Bunsen  photometer  —  "  foot  candles  " 

—  laws  of  regular  reflection  —  plane  mirrors — concave  mirrors 

—  convex  mirrors  —  graphical  construction  of  image  —  size  of 
image  —  the  mirror  formula. 

407.  Problem  of  illumination.     We  have  to  do  so  much  of 
our  work  and  play  by  lamplight,  that  we   ought  to  know 
something  about  illumination.     Of  course  the  first  essential 
is  to  have  enough  light  to  see  things  distinctly.     Further- 
more, experience  shows  that  we  may  have  enough  light  and 
yet   not  be  able   to   distinguish  the  position  and   shape  of 
objects  well,  because  the  lamps  are  not  properly  distributed 
to  cast  such  shadows  as  we  are  accustomed  to.     Then  there  is 
the  very  difficult  problem  of  getting  lamplight  which  will 
give  colored  objects  the  same  appearance  which  they  have  in 
daylight.     Finally,  we  have  to  protect  our  eyes  from  the 
glare  of  the  modern  powerful  electric  and  gas  lamps,  which 
are  likely  to  give  us  too  much  light  in  spots.     Besides  these 
purely  physical  aspects  of  the  problem  of  illumination,  we 
have  the  economic  question  of  its  cost. 

408.  Some  optical  terms.     We   all   know  that  we  cannot 
see  things  in  a  perfectly  dark  room  and  that  the  something 
which   enables  us  to  see  things  is  light.     There  are  some 
objects,  such  as  the  sun,  the  stars,  and  lamps,  which  we  can 
see  because  they  are  luminous,  but  almost  everything  that  we 

405 


406 


PRACTICAL   PHYSICS 


see  is  visible  because  of  the  light  which  falls  upon  it  and 
then  comes  from  it  to  the  eye.  Such  objects  are  illuminated. 
For  example,  we  can  see  the  pages  of  this  book,  if  they  are 
sufficiently  illuminated,  and  if  no  obstacle  is  put  between 
them  and  the  eye.  We  know  that  light  passes  through 
some  substances,  like  water,  glass,  and  air,  which  are  called 
transparent,  and  that  practically  no  light  gets  through  other 
substances,  such  as  wood  and  iron,  which  are  called  opaque. 

Between  transparent  and  opaque  substances  there  is,  how- 
ever, no  sharp  line  ;  for  example,  we  ordinarily  think  of 
water  as  transparent,  and  yet  in  the  depths  of  the  ocean 
utter  darkness  prevails.  On  the  other  hand,  some  opaque 
substances  transmit  light  if  cut  in  thin  enough  sections  ;  for 
example,  thin  gold  foil  appears  green  when  looked  through. 
In  general,  light  is  in  part  turned  back  or  reflected  by  sub- 
stances, in  part  transmitted,  and  in  part  absorbed.  An  object 
which  absorbs  all  the  light  falling  upon  it  is  called  black. 

409.  Light  advances  in  straight  lines.  Everybody  knows 
by  experience  that  it  is  impossible  to  see  around  a  corner. 

This  is  because  light 
under  ordinary  cir- 
cumstances advances 
in  straight  lines. 


If  we  set  up  a  screen  S 
and  a  candle  C,  as  shown 
in  figure  376,  with  an 
opaque  screen  0  pierced  by 
a  pin  hole  in  between,  we 
see  an  inverted  image  of 
the  flame.  This  shows 

that  the  light  goes  through  the  hole  in  straight  lines.     Simple  "  pinhole  " 

cameras  are  sometimes  made  on  this  principle. 


FIG.  376.  —  Light  travels  in  straight  lines. 


The  precise  measurement  of  angles  by  surveyors  depends 
upon  the  fact  that  light  comes  from  the  distant  object  to  the 
observer's  instrument  in  straight  lines. 


LIGHT:    LAMPS  AND  REFLECTORS 


407 


FIG.  377.  —  Shadow  cast  by  the  earth. 


Another  consequence  of  this  fact  is  the  formation  of  a 
shadow  when  an  opaque  object  obstructs  the  passage  of  light. 
The  edge  of  the  shadow  is,  however,  a  sharply  denned  tran- 
sition between  light  and  dark,  only  when  the  source  of  light 
is  very  small.  For  ex- 
ample, the  shadows  cast 
by  an  arc  lamp  are  more 

sharply  defined  than  those  V  ^^ — -  Earth 
cast  by  a  gas  flame  or  a 
Welsbach  mantle.  This 
is  also  shown  in  the  case  of  the  shadow  cast  by  the  earth,  as 
shown  in  figure  377.  The  region  A  is  in  the  full  shadow  and 
is  called  the  umbra,  while  in  the  region  BB,  on  either  side,  the 
light  grades  off  from  full  shadow  to  full  illumination.  This 
region  is  called  the  penumbra.  When  the  moon  happens  to 
get  wholly  inside  the  umbra,  we  have  what  is  called  a  total 
eclipse  of  the  moon.  When  the  moon  is  partly  in  the 
penumbra,  the  eclipse  is  partial. 

410.  Intensity  of  illumination  :  law  of  inverse  squares.  It 
scarcely  needs  to  be  stated  that  a  book  is  more  brilliantly 
illuminated  when  it  is  held  near  a  lamp  than  when  it  is  held 
far  from  the  same  lamp.  In  other  words,  the  intensity  of 
illumination,  that  is,  the  amount  of  light  falling  on  a  unit 
area,  decreases  when  the  distance  increases. 


FIG.  378.  —  Intensity  decreases  as  the  square  of  the  distance. 

Let  a  sheet  of  metal  which  has  in  it  a  small  pinhole  P  (Fig.  378)  be 
set  up  in  front  of  a  flame,  so  that  the  source  of  light  may  be  considered 


408  PRACTICAL  PHYSICS 

a  point.  Then,  one  foot  away,  let  us  put  a  piece  of  cardboard  A  which 
has  a  hole  in  it  one  inch  square.  At  a  distance  of  tivo  feet  from  the  pin- 
hole,  we  will  put  a  screen  B.  It  is  evident  that  the  light  which  passes 
through  the  inch  hole  in  A  is  spread  at  B  over  a  2-inch  square ;  that  is, 
over  4  square  inches.  If  we  move  the  screen  B  so  that  it  is  3  feet  from  P, 
the  light  which  passes  through  the  inch  hole  at  A  is  spread  over  a  3-inch 
square ;  that  is,  over  9  square  inches.  The  areas  of  these  squares  increase 
as  the  square  of  the  distance.  But  the  amount  of  light  falling  on  each 
total  area  is  the  same.  Therefore  the  amount  on  each  square  inch  de- 
creases as  the  square  of  the  distance. 

Intensity  of  illumination  (like  the  intensity  of  sound  and  for 

the  same  reason)  varies  inversely  as  the  square  of  the  distance. 

This  law  assumes  that  the  source  of  light  is  a  point,  and 

that  the  surface  is  placed  at  right  angles  to  the  rays  of  light. 

In  all  practical  cases,  however, 
the  source  of  light  is  a  surface 
or  region,  every  point  of  which 
is  giving  light,  and  in  such  cases 
this  law  is  only  approximately 
true.  When  the  receiving  sur- 
face is  inclined  (Fig.  379),  it 
FIG.  379. —  Surface  not  at  right  does  not  receive  as  much  light 

per  square  inch  as  when  held  at 
right  angles,  and  allowance  has  to  be  made  for  this  fact. 

411.  Illuminating  power  of  a  lamp.  In  computing  the 
amount  of  light  received  on  a  given  area  we  have  to  con- 
sider not  only  the  distance  from  the  source,  but  also  the 
illuminating  power  of  the  lamp  itself.  A  room,  for  example,  is 
much  more  brilliantly  illuminated  by  a  modern  electric  or 
gas  lamp  than  by  a  kerosene  lamp.  Since  there  are  now 
many  different  forms  of  lamps  on  the  market,  and  every 
householder  has  to  buy  some  kind  of  lamp,  it  is  highly  im- 
portant that  we  have  some  way  of  measuring  the  illuminat- 
ing power  of  a  lamp.  To  do  this  we  must  have  a  standard 
lamp  and  some  instrument  for  the  comparison  of  lamps,  that 
is,  a  photometer. 


LIGHT:    LAMPS  AND  REFLECTORS  409 

412.  The  standard  lamp.     Although  many  standard  lamps 
have  been  proposed,  none  are  altogether  satisfactory.     The 
oldest  standard  lamp,  which  is  still  used  in  calculation,  but 
seldom  in  actual  practice,  is  the  English  standard  candle, 
which  is  a  sperm  candle  made  according  to  certain  specifica- 
tions.    The  illuminating  power  of  a  horizontal  beam  from 
this  candle  is  called  a  candle  power. 

The  present  value  of  the  candle  power  as  used  in  the 
United  States  is  that  established  by  a  set  of  standard  incan- 
descent lamps  maintained  at  the  Bureau  of  Standards  in 
Washington,  D.C.  This  unit  of  intensity  is  called  the 
international  candle,  and  has  been  accepted  by  England  and 
France.  In  Germany  the  legal  unit  of  intensity  is  the 
Hefner,  which  is  equal  to  0.9  international  candles. 

In  testing  gas,  sperm  candles  are  still  used  in  routine 
work,  although  the  intensity  of  so-called  standard  candles 
may  vary  by  as  much  as  5  per  cent.  For  more  accurate 
work,  the  pentane  lamp  is  coming  into  use.  The  Harcourt 
form  of  this  lamp  burns  a  mixture  of  air  and  pentane  vapor 
and  has  an  intensity  of  10  candles. 

The  ordinary  open  gas  flame  consumes  from  5  cubic  feet 
of  gas  per  hour  upward  and  gives  from  15  to  25  candle 
power.  In  Massachusetts  the  legal  standard  for  gas  is  that 
it  shall  give  15  candle  power  in  a  burner  consuming  5  cubic 
feet  an  hour.  The  gas  tested  by  the  state  in  1911  averaged 
18.42  c.  p.  Welsbach  lamps  consume  only  about  3  cubic  feet 
of  gas  per  hour  and  give  from  50  to  100  candle  power. 

413.  Bunsen  photometer.     This  is  an  instrument  for  com- 
paring the  illuminating  power  of  a  beam  from  a  given  lamp 
with  the  illuminating  power  of  a  horizontal  beam  from  a 
standard   lamp.      This   "  grease-spot "    photometer   was  in- 
vented by  the  great  German  chemist,  Robert  Bunsen.     It 
consists  essentially  of  a  white  paper  screen  with  a  translucent 
spot  in  the  center,  which  transmits  light  freely.     The  screen 
is  placed  between  the  lamps  to  be  compared,  so  that  one  side  is 


410  PRACTICAL  PHYSICS 

lighted  by  one  lamp  and  one  by  the  other.  If  the  screen 
is  lighted  more  on  one  side,  that  side  appears  bright  with  a 
dark  spot  in  the  center,  while  the  other  side  is  darker  with  a 
bright  spot  in  the  center.  If  the  two  sides  are  equally  illu- 
minated, the  spot  disappears,  or  at  least  looks  equally  bright 
on  each  side.  The  arrangement  of  the  Bunsen  photometer 


T     ft  1  I\     T 

~T          ~T~ 


D 

FIG.  380.  —  Bunsen  photometer. 

is  shown  in  figure  380.     The  grease-spot  screen  is  inclosed  in 
a  box,  shown  in  figure  381,  which  is  open  at  the  ends  A  and 
B  toward  the  lamps  to  be  compared. 
The  eye  is  held  in  front  at  E.     Two 
mirrors,  m1  and  m^  are  placed  on  either 
side  of  the  screen,  as  indicated  in  the 
figure,  so  that  the  two  sides  of  the 
screen  can  be  seen  at  the  same  time. 
FIG.  381. -Bunsen light  box        414.    Use    of    Bunsen     photometer. 
The  photometer  must   be   used  in  a 

dark  room  or  else  in  light-tight  box.  The  lamp  X  to 
be  tested  is  placed  at  one  end  of  the  photometer  bar  and 
the  standard  lamp  S  at  the  opposite  end.  The  screen  is 
then  moved  back  and  forth  until  a  position  is  found  where  it 
is  equally  illuminated  on  both  sides,  and  the  distances  A  and 
B  are  measured. 

It  is  evident  that  if  the  distances  A  and  B  are  equal,  the 
candle  powers  of  the  two  lamps  are  the  same.  If  the  dis- 
tances are  not  equal,  the  lamp  which  is  farther  from  the  screen 


LIGHT:    LAMPS  AND  REFLECTORS 


411 


has  the  greater  candle  power.  Furthermore,  since  the  intensity 
of  illumination  decreases  as  the  square  of  the  distance,  the 
candle  powers  of  the  two  lamps  are  directly  proportional  to  the 
squares  of  their  distances  from  the  screen. 


For  example, 
and 

Let 
and 

Then 

so 


let  16  =  candle  power  of  lamp  S, 
X  =  candle  power  of  lamp  X. 
80  cm.  =  distance  of  screen  from  lamp  S, 
100  cm.  —  distance  of  screen  from  lamp  X, 


16        (80)2 

X  =  25  candle  power. 


415.  Distribution  of  light.  No  lamp  gives  light  uniformly 
in  all  directions.  Thus  in  the  ordinary  kerosene  lamp  the 
burner  and  oil  reservoir  cut 
off  the  light  which  would  be 
radiated  downward  from  the 
flame,  and  if  the  flame  is 
broad  and  thin,  it  will  give 
more  light  broadside  on  than 
edgewise.  Similarly  an  in- 
candescent lamp  gives  differ- 
ent intensities  in  different  di- 
rections because  of  the  shape 
of  the  filament. 

Since  an  incandescent  lamp 
can  be  easily  turr^d  in  any  po- 
sition (Fig.  382),  it  is  not  dif-  Fia 
ficult,  with  the  Bunsen  pho- 
tometer, to  measure  its  candle  power  in  various  positions.  If 
the  candle  power  is  measured  for  several  points  in  a  horizontal 
plane,  and'the  results  of  the  tests  averaged  up,  the  result  is 
called  its  mean  horizontal  candle  power.  Such  tests  show  that 
the  candle  power  in  various  directions  in  a  horizontal  plane 
does  not  vary  very  much.  In  a  factory  the  lamp  under 
test  is  rotated  around  a  vertical  axis  at  a  speed  of  about  300 


lamp 


412 


PRACTICAL  PHYSICS 


FIG.  383.  —  Curve  to  show 
vertical  distribution. 


revolutions  per  minute,  and  the  photometer  reads  directly  the 
mean  horizontal  candle  power  of  the  lamp.  A  "  16  candle 
power  lamp  "  means  a  lamp  of  which 
the  mean  horizontal  intensity  is  16 
candles. 

If  the  lamp  to  be  tested  is  tilted  at 
various  angles  in  a  vertical  plane,  the 
results  show  that  the  lamp  has  very 
low  candle  power  directly  under  the 
tip.  The  results  of  such  tests  may  be 
best  shown  graphically  by  a  diagram 
(Fig.  383).  In  this  figure  the  inten- 
sity of  the  light  in  various  directions  in  a  vertical  plane  is 
indicated  by  the  curve,  which  varies  in  its  distance  from  the 
center  of  the  concentric  circles  according  to  the  intensity  of 
the  light.  For  example,  the  candle  power  directly  under  the 
tip  of  the  bulb  (0°)  is  a  little 
under  8,  while  horizontally 
(90°)  it  is  16  candles. 

When  it  is  desirable  to 
throw  as  much  light  as  pos- 
sible directly  downward,  some 
kind  of  a  reflector  or  shade  is 
used.  Figure  384  shows  the 
vertical  distribution  of  light 
when  the  bulb  is  fitted  with  a 
special  shade.  From  this 
curve  it  will  be  seen  that  the 
horizontal  intensity  is  cut 
down  to  6  candles,  while  the 
downward  intensity  runs  over 
50  candles.  Such  shades,  made  in  a  great  variety  of  forms 
to  give  different  desirable  distributions,  make  it  possible  to 
work  out  scientifically  the  problem  of  lighting  a  given  room 
or  work  shop  efficiently. 


FIG.  384.  —  Vertical  distribution,  when 
fitted  with  shade. 


LIGHT:    LAMPS  AND   REFLECTORS  413 

416.  Measurement  of  intensity  of  illumination.  We  have 
just  seen  that  the  unit  of  intensity  for  a  source  of  light  is 
the  international  candle.  The  illumination  which  such  a 
standard  candle  throws  upon  a  surface  placed  one  foot  away 
and  at  right  angles  to  the  rays  of  light  is  called  a  foot  candle. 
It  is  the  unit  of  intensity  of  illumination.  For  example,  a  16 
candle-power  lamp  would  illuminate  a  surface  placed  1 
foot  from  it  with  an  intensity  of  16  foot  candles.  Again  if 
the  lamp  were  a  32  candle  power  lamp  and  the  object  were 
4  feet  away,  the  intensity  of  illumination  would  be  32 
divided  by  (4)2,  or  2  foot  candles. 

In  these  examples  we  have  assumed  that  there  is  only  one 
source  of  illumination  and  that  the  surface  is  perpendicular 
to  the  rays  of  light.  In  practice  this  is  almost  never  the 
case,  so  that  the  problem  of  computing  or  measuring  the  in- 
tensity of  illumination  on  any  given  surface  is  very  difficult. 
One  reason  for  this  difficulty  is  that  we  have  as  yet  no  satis- 
factory simple  instrument  for  measuring  intensity  of  illu- 
mination directly. 

The  amount  of  illumination  needed  to  furnish  "  good  light 
to  see  by  "  varies  greatly  with  conditions.  For  example, 
drafting  rooms,  theater  stages,  and  stores  require  about  4  foot 
candles  ;  while  churches,  residences,  and  public  corridors  may 
need  but  1  foot  candle.  Excessive  light  is  as  undesirable  as 
not  enough.  Exposed  light  sources  of  great  brilliancy  (more 
than  5  candle  power  per  square  inch)  constitute  a  common 
source  of  eye  trouble.  To  avoid  this,  electric  bulbs  should 
be  frosted  and  distributed  in  small  units,  or  covered  with 
shades  which  diffuse  the  light,  or  else  concealed  entirely  from 
view,  in  which  case  the  illumination  is  obtained  by  light  re- 
flected from  the  ceiling  and  walls.  This  indirect  system  of 
illumination  gives  by  far  the  best  light,  especially  for  large 
rooms  in  public  buildings,  but  costs  more  than  other  systems, 
and  is  to  be  regarded  as  a  luxury. 


414  PRACTICAL  PHYSICS 

PROBLEMS  „ 

1.  If  the  page  of  your  book  is  sufficiently  illuminated  at  a  distance  of 
3  feet  from  an  8  candle  power  lamp,  how  many  candle  power  will  be 
needed  when  you  move  2  feet  farther  away  ? 

2.  If  a  photographic  print  can  be  made  in  30  seconds  when  held  3 
feet  from  a  light,  how  long  an  exposure  will  be  needed  when  the  print  is  6 
feet  away  ? 

3.  A  4  candle  power  lamp  is  120  centimeters  from  a  screen.     How  far 
away  must  a  16  candle  power  lamp  be  to  illuminate  the  screen  equally? 

4.  In  measuring  the  candle  power  of  a  lamp,  a  Hefner  standard  lamp 
(0.90  candle  power)  is  50  centimeters  from  the  grease  spot  of  a  Bunsen 
photometer,  and  the  lamp  to  be  tested  balances  it  when  150  centimeters 
from  the  grease  spot.     How  many  candle  power  has  the  lamp  ? 

5.  Two  lamps  are  16  and  32  candle  power  respectively,  and  are  200 
centimeters  apart.     Where  between  the  lamps  may  a  grease-spot  pho- 
tometer screen  be  placed  for  its  two  sides  to  be  equally  illuminated  ? 

6.  What  is  the  illumination  in  foot  candles  on  a  surface  5  feet  from  an 
80  candle  power  lamp  ? 

7.  The  necessary  illumination  for  reading  is  about  2  foot  candles.  How 
far  away  may  a  16  candle  power  lamp  be  placed? 

8.  If  the  lamp  with  the  special  shade  described  in  section  415  were 
hung  above  a  reading  table,  how  high  should  it  be  hung  ?     (See  curve  of 
distribution,  Fig.  384.) 

9.  Compare  the  cost  of  illumination  with  gas  and  electricity.     A  gas 
jet  burning  5  cubic   feet  of  gas  per  hour  gives  a  flame  of  18  candle 
power.     The  gas  costs  85  cents  per  1000  cubic  feet.     A  16  candle  power 
lamp  consumes  40  watts.     Electricity  is  10  cents  per  kilowatt  hour. 

417.  Reflectors,  regular  and  irregular.  We  have  already 
said  that  we  are  able  to  see  most  objects  about  us  by  the  light 
which  they  reflect  to  our  eyes.  The  surface 
of  visible  objects  is  rough,  and  so  the  light 
striking  the  irregular  surface  is  reflected  in 
an  irregular  fashion,  as  shown  in  figure  385. 
This  kind  of  reflection  or  turning  back  of 
the  Hght  we  cal1  diffused  reflection.  Thus  the 
light  striking  a  piece  of  paper  or  unvar- 
nished wood  is  scattered.  If,  however,  light  strikes  a  flat 
metallic  surface  so  carefully  polished  that  it  is  very  smooth, 


LIGHT:    LAMPS  AND  REFLECTORS 


415 


the  light  comes  to  the  eye  as  though  coming  directly  from  a 
distant  object,  instead  of  from  the  reflecting  surface.  This  is 
called  regular  reflection,  and  is  illustrated  in  figure  386,  where 
mm  is  the  reflecting  surface  or  mirror.  The  line  OP  in- 
dicates the  direction  of  the  light  falling  on  the  mirror  and 
PE  indicates  the  direction  of  the  reflected  light. 

418.  Law  of  reflection.  When  light  comes  through  a  small 
opening,  the  stream  of  light  is  called  a  beam.  A  narrow  beam 
may  be  called  a  ray.*  When  a  beam  of  light  comes  from  a 
very  distant  source,  such  as  the  sun,  the 
rays  of  which  it  is  composed  are  parallel, 
and  so  it  is  called  a  parallel  beam. 

In  figure  386,  let  OP  be  the  direction  of  a 
parallel  beam  striking  the  mirror  mm  obliquely, 
and  PE  that  of  the  reflected  beam.  If  a  line 
nn,  called  the  normal,  is  drawn  perpendicular  to 
the  reflecting  surface  at  the  point  P,  the  angle 
between  the  normal  and  the  direction  OP  of  the 
incident  beam  is  called  the  angle  of  incidence, 
and  the  angle  between  the  normal  and  the 
direction  of  the  reflected  beam  is  called  the  angle  of  reflection. 

Careful  experiments  have  shown  that,  whatever  the  size 
of  these  angles, 

I.    The  incident  ray,  the  normal,  and  the  reflected  ray  lie 
in  one  plane. 

II.  The  angle  of  incidence  is  equal 
to  the  angle  of  reflection. 

419.  Images  in  a  plane  mirror.  We 
all  know  that  if  one  stands  in  front  of 
a  plane  mirror,  he  sees  his  own  image 
and  that  of  the  objects  about  him,  as  if 

FIG.  387.  -Image  in  a  plane     they  were  behind  the  ™irror.      In  figure 
mirror.  387  we  see  that  light  coming  from  any 


FIG.  386.  — Regular  re- 
flection from  smooth 
surface. 


Object 


*  A  more  accurate  definition  of  a  "ray  "  will  be  given  in  section  437  of  the 
next  chapter. 


416  PRACTICAL  PHYSICS 

point  A  of  an  object  is  reflected  by  the  mirror  to  the  eye  as  if 
coming  from  a  point  A'  back  of  the  mirror.  Similarly,  light 
coming  from  a  group  of  points  (an  object  AS)  seems  to  come 
from  a  similar  group  of  points  (the  image  A B')  back  of  the 
mirror.  The  group  of  points  from  which  the  light  appears 
to  come  is  called  the  image  of  the  object.  A  line  AA  drawn 
from  any  point  in  the  object  to  its  corresponding  point  in  the 
image  is  perpendicular  to,  and  is  bisected  by,  the  mirror  mm. 
In  general,  the  image  of  an  object  in  a  plane  mirror  is  the 
same  size  as  the  object,  and  as  far  behind  the  mirror  as  the 
object  is  in  front. 

Indeed,  such  an  image  is  so  much  like  a  real  object  that 
conjurors  often  make  use  of  the  illusions  due  to  the  invisibility 
of  a  well-polished  mirror.  It  should,  however,  be  remem- 
bered that  the  image  is  reversed  from  right  to  left,  as  is  seen 
when  a  printed  page  is  held  in  front  of  a  mirror,  so  that  in 
conjuror's  tricks  no  letters  or  clock  faces  are  allowed  to  be 
seen  in  mirrors. 

420.  Uses  of  plane  mirrors.  Good  mirrors  for  household 
use  are  made  of  plate  glass  backed  by  a  thin  coating  of  silver 

or  mercury.  Only  a  very  small 
fraction  of  the  light  is  reflected 
from  the  front  surface  of  the 
glass;  the  rest  is  reflected  from 
the  metal  back. 

Large  plate-glass  mirrors  are 
sometimes  placed  in  the  walls  of 
public  places  to  give  the  impres- 
sion of  spaciousness.  In  scien- 
tific instruments  a  very  small 

FIG.  388. -Sextant  used  to  meas-     mirror   •       ften  attached  to  a  ro_ 
ure  angles. 

tating  part,  such  as  the  coil  01  a 

galvanometer.  Such  a  mirror  will  turn  a  reflected  beam  of 
light  through  twice  the  angle  through  which  the  mirror  itself 
is  turned.  A  rotating  mirror,  M,  is  an  essential  part  of  the 


LIGHT:    LAMPS  AND  REFLECTORS  417 

sextant  which  the  mariner  uses  to  get  the  altitude  of  the  sun. 
By  means  of  a  heliostat,  which  is  simply  a  plane  mirror 
turned  by  clockwork  so  as  to  keep  up  with  the  sun,  the 
sun's  rays  may  be  reflected  into  a  room,  through  an  opening 
in  the  wall,  for  projection  purposes. 

421.  Curved  mirrors.     A  curved  mirror  is  usually  spheri- 
cal ;  that  is,  it  is  a  portion  of  the  surface  of  a  sphere.     If  it 

is  a  portion  of  the  outer  surface,  it  is  ^ -^ 

called  a  convex  mirror ;  if  it  is  a  por- 
tion of  the  inner  surface,  it  is  called  a      f 

concave  mirror.       The   center   of   the      j 
sphere,  of  which  the  curved  mirror      \ 
is  a  portion,  is  called  the  center  of  cur- 
vature ((7  in  Fig.  389).     The  line  CM         ^^_ 
connecting  the  middle  of  the  mirror    FIG.  389.— Center  of  a  curved 
M  with  the  center  of  curvature  Q  is  mirror, 

called  the  principal  axis.  Any  other  straight  line  through  the 
center  of  curvature,  such  as  OS,  is  called  a  secondary  axis.  It 
will  be  noted  that  any  axis  is  perpendicular  to  the  reflecting 
surface. 

422.  Principal  focus.     When  a  beam  of  light  parallel  to 
the  principal  axis  strikes  a  concave  mirror,  the  rays  are  so 

reflected  as  to  pass  through, 
or  very  close  to,  a  single 
point  (.Fin  Fig.  390). 

This  point  is  called  the 
principal  focus  of  the  mirror. 
It  may  be  defined  as  that 
point  where  all  rays  parallel 

FIG.  390.  —  Concave  mirror  converges  par-     fo  and  near  the  principal  axis 
allel  rays.  /.,  /,     , . 

meet  after  reflection. 

The  principal  focus  is  located  halfway  between  the  mirror 
and  its  center  of  curvature. 

Suppose  the  ray  QP  in  figure  391,  parallel  to  the  axis  AB,  strikes  the 
mirror  at  the  point  P  and  is  reflected  back  in  the  direction  PF,  so  as  to 

2E 


418 


PRACTICAL   PHYSICS 


make  the  angle  of  incidence  i  equal  to  the  angle  of  reflection  r.  Since 
QP  and  AB  are  parallel  lines,  the  angle  i  is  equal  to  the  angle  a.  There- 
fore the  angle  a  must  be  equal  to  the 
angle  r,  and  CF  =  PF.  But  when  P  is 
near  0,  PF  is  nearly  equal  to  FO,  which 
means  that  F  is  about  midway  between 
C  and  0.  It  can  be  proved  that  the 
principal  focus  which  is  very  close  to  F 
is  exactly  halfway  between  C  and  0. 


FIG.  391. 


Location  of  principal 
focus. 


A 


FIG.  392.  —  Aberration  in 
spherical  concave  mirror. 


The  distance  from  the  princi- 
pal focus  to  the  mirror  is  called 
the  focal  length  of  the  mirror  and 
is  one  half  the  radius  of  curvature. 

All  the  rays  parallel  to  the  principal  axis  of  a  concave 
spherical  mirror  do  not  meet  exactly  at 
the  same  point  after  reflection.  This 
failure  of  the  rays  to  converge  accu- 
rately at  a  point  is  called  sp^ericaLaber- 
ration.  This  imperfection  is  slight 
when  only  a  small  portion  of  a  sphere 
is  used  as  a  mirror.  Spherical  aber- 
ration in  a  large  mirror  is  shown  in 
figure  392,  where  it  will  be  observed 
that  only  the  central  rays  are  reflected  through  the  focus  F, 
while  the  rays  which  strike  the  mirror  near  the  edge  are  bent 
decidedly  to  the  right  of  F. 

It  is  sometimes  necessary,  as  in  the 
case  of  a  searchlight,  to  take  the  diver- 
gent rays  of  an  arc  lamp  and  reflect 
them  all  in  one  direction.    This  can  be 
done  roughly  with  a  concave  spherical 
mirror,  by  putting  the  arc  at  the  prin- 
cipal focus ;  for  then  the  rays  travel  the 
same  paths  as  above,  but  in  the  opposite 
FIG.  393-Paraboiic       direction.     To  avoid  spherical  aberra- 
mirror.  tion,  however,  a  parabolic  mirror  (Fig.  393) 


\ 


\ 


A 


y 


LIGHT:    LAMPS  AND  REFLECTORS 


419 


is  generally  used.     These  mirrors  are  also  used  in  the  head- 
lights of  locomotives  and  automobiles. 

423.  Applications  of  concave  mirrors.  The  ophthalmoscope  is 
a  concave  mirror  with  a  little  hole  in  its  center.  With  this 
instrument  a  physician  is  able  to  reflect  light  from  a  lamp 
into  a  patient's  eye,  and  at  the  same  time  to  look  through 
the  hole  into  the  eye  thus  illuminated. 


.    FIG.  394.— Reflecting  telescope. 

A  certain  type  of  telescope,  called  a  reflecting  telescope,  con- 
sists of  a  long  tube  with  a  concave  mirror  mn  at  one  end, 
which  forms  an  image  of  a  distant  object.  The  only  pur- 
pose of  the  tube  is  to  support  near  its  open  end  an  eyepiece 
or  magnifying  glass,  E,  through  which  the  image  can  be 
advantageously  examined. 

In  a  compound  microscope  the  light  from  a  window  or  lamp 
is  concentrated  upon  the  small  object  to  be  examined  by 
means  of  a  concave  mirror. 

We  have  already  stated  that 
concave  mirrors  are  extensively 
used  in  searchlights  and  headlights. 

424.  Convex  mirror.  When 
a  beam  of  light  parallel  to  the 
principal  axis  strikes  a  convex 
mirror,  the  rays  are  reflected 
as  if  they  came  from  a  point 
behind  the  mirror.  This  is 
shown  in  figure  395,  where  0  is  the  center  of  curvature 
and  F  is  the  point  from  which  the  reflected  rays  diverge. 
The  point  F  is  called  a  virtual  focus  because  the  rays  do  not 


FIG.  395.  —  Convex  mirror  and  virtual 
focus. 


420 


PRACTICAL   PHYSICS 


actually  pass  through  it,  but  simply  look  as  if  they  had  come 
from  it.  In  the  case  of  the  concave  mirror  the  rays  do  ac- 
tually pass  through  the  point  F,  as  shown  by  the  fact  that  a 
large  concave  mirror  of  short  focal  length  causes  so  great  a 
concentration  of  the  sun's  radiant  energy  that  paper  and 
wood  may  be  ignited  if  placed  at  F.  Such  a  focus  is  a  real 
focus. 

425.    Construction  of  images.     It  is  possible  to  learn  a  great 
deal  about  the  position  and  size  of  images  formed  by  mirrors, 

by  carefully  constructing  dia- 
grams to  show  the  paths  of  the 
rays  of  light. 

Suppose  mn  in  figure  396  is  a  convex 
mirror,  and  AB  an  object.  Let  us 
draw  A  C,  a  ray  normal  to  the  mirror. 
This  ray  will  be  reflected  directly  back 
on  itself.  Again  let  us  draw  AL  par- 
allel to  the  principal  axis.  This  ray 
FIG.  396. — Image  in  a  convex  mirror.  .„  ,  a  ,  ,  ..  .,  ,. 

will  be  reflected  as  if  it  came  from  F. 

The  image  point  of  A  will  be  where  these  two  reflected  rays  cross ;  that 
is,  at  Af.  Another  ray  from  A  that  might  be  used  in  this  construction  is 
the  ray  through  F.  It  would  be  reflected  parallel  to  the  axis  and  would 
also  pass  through  A'. 

This  construction  shows  that  the  image  in  a  convex  mirror 
always  seems  to  be  behind  the  mirror  and  smaller  than  the 
object.  It  is  erect  and  is  nearer  the  mirror  than  the  object  is. 
It  is  always  a  virtual  image. 
Thus  one  sees  a  virtual  image 
of  his  face  in  a  polished  ball. 
It  is  always  right  side  up  and 
of  small  size. 

Suppose  MON  (Fig.  397)  is  a 
concave  mirror,  of  which  C  is  the 
center  of  curvature.  Let  AB  be  an 
object  which  is  placed  beyond  the 
center  of  curvature.  To  determine  the  position  of  the  image,  let  us  trace 
two  rays  from  A.  The  point  A',  where  they  intersect  after  reflection,  is 


397>_Construction  of  im       in  con. 
cave  mjrror< 


LIGHT:    LAMPS  AND  REFLECTORS 


421 


the  image  of  A.  If  AN  is  one  such  ray  passing  through  C,  it  will  hit  the 
mirror  perpendicularly  and  be  reflected  back  along  the  line  .ZVC.  If  the 
other  ray  from  A  is  AM,  parallel  to  the  axis,  it  will  be  reflected  so  as  to 
pass  through  the  focus  F.  Since  B  is  on  the  axis,  its  image  B'  will  also 
be  on  the  axis  ;  so  that  the  image  of  the  arrow  AB  will  be  the  arrow  A'B'. 
Another  ray  from  A  that  might  be  used  in  this  construction  is  the  ray 
through  F.  It  would  be  reflected  parallel  to  the  axis  arid  would  also 
pass  through  A'. 

It  will  be  seen  that  when  the  object  is  beyond  the  center  of 
curvature,  the  image  is  inverted  and  in  front  of  the  mirror. 
Since  the  rays  of  light 
from  A  really  do  pass 
through  Af,  the  image  is 
real. 

426. 
image. 


FIG.  398.  — To  get  the  size  of  a  real  image. 


Size    of    a    real 

Let  us  draw  the 
rays  AO  and  OA'  (Fig. 
398).  From  the  law  of 
reflection,  the  angle  of  in- 
cidence i  is  equal  to  the  angle  of  reflection  r.  Therefore, 
the  right  triangles  A  OB  and  A!  OB'  are  similar,  and  their  cor- 
responding sides  are  in  proportion.  That  is, 

AB       BO 


A'B1  ~~  B'  0' 


flhe 


The  size  of  the  image  is  to  the  size  ojihe  object  as  the  distance 
of  the  image  from,  the  mirror  is  to  the  distance  of  the  object 
from  the  mirror.  ' 

427.  Conjugate  foci.  We  have  seen  that  when  A  is  the 
object  point,  the  image  point  is  at  A' .  But  figure  397  shows 
that  if  A!  is  the  object  point,  the  image  point  is  at  A ;  for 
the  rays  will  travel  the  same  paths  in  the  other  direction. 
For  example,  if  a  candle  were  put  at  AB,  an  inverted  smaller 
image  would  be  formed  on  a  screen  placed  at  A  B'  ;  also  if 
the  candle  were  put  at  AB',  the  image  would  be  inverted, 
larger,  and  located  at  AB. 


422 


PRACTICAL  PHYSICS 


FIG.  399. -Construction  of  virtual  image 
in  concave  mirror. 


Two  points,  so  situated  that  light  from  one  is  concentrated 
at  the  other,  are  called  conjugate  foci.  For  example,  B  and  B' 
are  two  such  points  and  therefore  are  conjugate  foci. 

428.  Virtual  image  in  a  concave  mirror.     We  have  just 
seen  that  when  the  object  is  beyond  the  center  of  curvature, 
the  image  is  between  the  principal  focus  F  and  the  center  of 
curvature  C.     Also  when  the  object  is  between  F  and  (7,  the 

image  is  beyond  C.  In 
both  these  cases,  the  image 
is  real ;  that  is,  the  image 
is  always  real  when  the  ob- 
ject is  outside  the  principal 
focus  F. 

When,  however,  the  ob- 
ject is  placed  inside  the  prin- 
cipal focus,  that  is,  between 
F  and  M,  as  shown  in  figure 
399,  the  image  is  behind  the  mirror,  erect,  enlarged,  and  virtual. 

To  show  this  we  may,  as  before,  trace  two  rays  from  the  point  A,  one 
parallel  to  the  axis,  which  is  reflected  through  F,  and  the  other  perpen- 
dicular to  the  mirror,  which  is  reflected  back  on  itself  through  C.  They 
will  diverge  after  reflection  and  must  be  produced  backward  to  find  the 
point  of  intersection  A'.  The  image  A'  is  a 
virtual  image,  because  the  light  from  A  does 
not  actually  pass  through  A'. 

429.  Size  of  a  virtual  image.    Since 
every  ray  from  A  (Fig.  400)  is  re- 
flected so  as  to  seem  to  come  from 
A',  the  ray  from  A  to  M,  the  middle 
of  the  mirror,  will  be  reflected  in  the 
direction  A1 MO.     Since  the  angles  of    FlG< 
incidence  and  reflection  are  equal, 

Angle  AMB  =  angle  BMC. 

But  A' MB'  and  BMC  are  vertical  angles  and  equal.     So 
Angle  AMB= angle  A' MB' . 


LIGHT:    LAMPS  AND  REFLECTORS  423 


Therefore  the  right  triangles  AMB  and  A! MB1  are  similar, 
and  A'B'      B'M 


AB  "  BM' 

So  in  this  case,  as  before,  the  size  of  the  image  is  to  the  size  of 
the  object,  as  the  distance  of  the  image  from  the  mirror  is  to  the 
distance  of  the  object  from  the 
mirror. 

430.  The  mirror  formula. 
Let  0  be  an  object  on  the 
axis,  OM  any  ray  from  0 
meeting  the  mirror  at  M. 
Draw  the  radius  CM  and 

,  T  a          j  FIG.  401.  —  Real  image  in  concave  mirror. 

construct   the   reflected   ray 

MI,  making  angle  OMG=  angle  OMI.     Then  Jis  the  image  of 

0.    Since  CM  is  the  bisector  of  the  angle  OMI,  it  follows  that 


IM      1C' 

Let  TN=Dl}   and    ON=D0.     When   the   aperture,   that  is,  the 
angle  MON,  is  small,  we  have  the  approximate  relations 

OM=ON=D0,  and  IM=IN=Dl. 
Now,  since  FN=f, 

00=  ON-  CN=D0-  2f, 
IC  =  CN-IN=2f-Dl. 
Substituting  these  values  in  the  proportion  (1),  we  have 


A     2  /- 

and  so  Dlf+  D0f=  D0D^. 

Dividing  by  D0  x  A  X/,  we  have 

JL  +  1,^1 

Do     D,     f 

where 

DQ  =  distance  of  object  from  mirror, 
Dl  =  distance  of  image  from  mirror, 
f=  focal  length  of  mirror. 


424  PRACTICAL  PHYSICS 

Stated  in  words 

1  1 


Object  distance     Image  distance     Focal  length 

This  equation  gives  a  relation  between  the  distance  of  the 
object,  the  distance  of  the  image,  and  the  focal  length.  If 
any  two  of  these  three  quantities  are  known,  the  third  can 
be  calculated. 

It  can  be  proved  that  this  equation  holds  as  it  stands  for 
all  cases  of  images  either  real  or  virtual,  formed  in  a  concave 
mirror.  If  the  value  of  DL  comes  out  negative,  for  certain 
values  of  D0  and  /,  as  it  will  when  D0  is  less  than  /,  the 
meaning  is  that  the  image  is  behind  the  mirror;  that  is,  the 
image  is  virtual.  It  can  be  shown  that  it  holds  also  for  con- 
vex mirrors,  if  the  focal  length  /  of  a  convex  mirror  is 
regarded  as  negative. 

In  the  next  chapter  we  shall  see  that  the  same  formula 
holds  for  lenses. 

PROBLEMS 

1.  If  a  ray  of  light  strikes  a  plane  mirror  so  that  the  angle  between 
the  ray  and  the  mirror  is  25°,  what  is  the  angle  between  the  incident  and 
reflected  rays  ? 

2.  If  the  mirror  in  problem  1  is  turned  1°,  so  that  the  angle  between 
the  incident  ray  and  the  mirror  becomes  26°,  through  how  many  degrees 
has  the  reflected  ray  been  turned  V 

3.  An  object  is  placed  15  inches  from  a  concave  mirror  whose  radius 
of  curvature  is  12  inches.     How  far  from  the  mirror  is  the  image  ?    Is  it 
real  or  virtual,  erect  or  inverted? 

4.  If  the  object  in  problem  3  is  4.5  inches  long,  how  long  is  the 
image  ? 

5.  An  object  is  placed  12  inches  from  a  concave  mirror  whose  focal 
length  is  8  inches.     How  far  from  the  mirror  is  the  image  ?    Is  it  real  or 
virtual,  erect  or  inverted  ? 

6.  If  the  object  in  problem  5  is  2  inches  long,  how  long  is  the  image? 

7.  An   arrow  1  inch  long  is  placed  4  inches  from  a  concave  mirror 
whose  radius  of  curvature  is  12  inches.     Find  the  position,  length,  and 
nature  of  the  image. 


LIGHT:  LAMPS  AND  REFLECTORS  425 

8.  If  the  image  of  a  candle  flame,  placed  10  inches  from  a  concave 
mirror,  is  formed  distinctly  on  a  screen  30  inches  from  the  mirror,  what 
is  the  radius  of  curvature  ? 

9.  How  far  from  a  concave  mirror,  whose  focal  length  is  2  feet,  must 
a  man  stand  to  see  an  erect  image  of  his  face  twice  its  natural  size? 

10.  Where  must  an  object  be  placed  to  form,  in  a  concave  mirror 
whose  focal  length  is  10  inches,  a  real  image  one  half  as  long  as  the 
object  ? 


SUMMARY    OF   PRINCIPLES    IN    CHAPTER    XXI 

Intensity  of  illumination  varies  inversely  as  the  square  of  the 
distance. 

Candle  powers  of  lamps  giving  equal  illumination  are  directly 
proportional  to  the  squares  of  their  distances  from  screen. 
(That  is,  lamp  farther  away  is  more  powerful.) 

Unit  intensity  of  illumination,  or  foot  candle,  is  illumination  due 
to  a  one  candle  power  lamp  one  foot  away. 

(Desirable  intensity  from  1  to  4  foot  candles.) 

In  regular  reflection:  — 

I.   Incident,  normal,  and  reflected  rays  all  in  one  plane. 
II.   Angle  of  reflection  =  angle  of  incidence. 

Plane  mirror:  Image  always  behind  mirror,  erect,  virtual,  same 
size  as  object,  and  at  same  distance  from  mirror  as  object. 

Principal  focus  of  curved  mirror  (either  concave  or  convex), 
Defined  as  convergence  point  for  rays  parallel  to  axis  of  mirror. 
Located  halfway  between  mirror  and  center  of  curvature. 

Concave  mirror  :  — 

If  object  is  outside  focus,  image  is  also  outside  focus,  and  center 
of  curvature  is  between  object  and  image.  Image  is  inverted 
and  real. 

If  object  is  inside  focus,  image  is  behind  mirror,  erect  and 
virtual. 

Convex  mirror  :  Image  always  behind  mirror,  erect  and  virtual. 


426  PRACTICAL  PHYSICS 

Mirror  formula  (holds  for  both  concave  and  convex  mirrors) :  — 


Object  distance     Image  distance     Focal  length 

For  concave  mirror,  focal  length  is  positive. 
For  convex  mirror,  focal  length  is  negative. 
For  real  image  in  front  of  mirror,  image  distance  comes  out 

positive. 
For  virtual  image  behind  mirror,  image   distance   comes   out 

negative. 

Size  rule  (holds  for  both  concave  and  convex  mirrors) :  — 
Length  of  image  _^  image  distance  (from  mirror) 
Length  of  object      object  distance  (from  mirror) 

QUESTIONS 

1.  What  is   the  difference  between   16  candle  power  and  16  foot 
candles  ? 

2.  Explain  how  a  Welsbach  gas  lamp  consuming  only  3  cubic  feet 
of  gas  per  hour  gives  over  50  candle  power,  while  the  ordinary  gas  jet 
uses  5  er  more  cubic  feet  per  hour  and  gives  only  about  18  candle  power. 

3.  If  light  from  a  very  distant  object,  such  as  the  sun,  falls  on  a 
concave  mirror,  where  is  the  image  formed? 

4.  How  does  the  curve  of  a  parabola  differ  from  the  arc  of  a  circle? 

5.  How  does  the  action  of  a  parabolic  mirror  differ  from  that  of  a 
concave  spherical  mirror. 

6.  What  is  the  danger  in  too  great  intensity  of  illumination? 

7.  Explain  how  the  image  of  a  man  standing  in  front  of  a  plane 
mirror,  which  is  tilted  so  as  to  make  an  angle  of  45°  with  the  floor, 
appears  horizontal. 

8.  A  person  looking  into  a  mirror  sees  a  very  small  image  of  his  face 
upside  down.     What  kind  of  mirror  is  it  ? 

9.  Show  by  a  diagram  how  a  tailor  arranges  two  mirrors  so  that 
a  customer  can  see  the  back  of  his  coat. 

10.  A  room  20  feet  square  has  plane  mirrors  on  opposite  walls.     A 
man  in  the  room  holds  a  candle  close  to  his  head.     Where  should  he 
stand  so  as  to  be  as  near  as  possible  to  the  twice  reflected  image  of  the 
candle  in  the  mirrors? 

11.  Why  is  an  image  in  a  plane  mirror  reversed  from  right  to  left, 
but  not  up  and  down  ? 


CHAPTER  XXII 

LENSES  AND  OPTICAL  INSTRUMENTS 

Refraction  —  law  of  refraction  —  velocity  of  light  —  wave 
fronts  —  explanation  of  refraction  —  index  of  refraction  as 
ratio  of  speeds  —  total  reflection  —  prism  —  lens  —  lens  for- 
mula—  size  rule  —  defects  of  lenses. 

Camera  —  projecting  lantern  —  moving  pictures  —  eye  —  de- 
fects of  eye  —  magnifying  glass  —  microscope  —  telescope  — 
erecting  telescope  —  opera  glass  —  prism  binocular. 

431.  Optical  instruments.     The   human   eye   is  the  most 
common  and  at  the  same  time  one  of  the  most  remarkable 
optical  instruments  known.     Human  eyes  are  often  imper- 
fect in  various  ways,  and  have  to  be  "  corrected,"  or  rather 
aided  in  their  work;  for  defective  eyes  themselves  are  seldom 
changed  by  spectacles  or  eyeglasses.     These,  too,  we  shall 
study  in  this  chapter.     Even  a  healthy  eye  has  its  limitations, 
and  many  optical  instruments  have  been  devised  to  help  it  to 
see  things  too  far  away  or  too  small  for  ordinary  vision. 
And  finally,  there  are  many  devices,  such  as  cameras,  stereop- 
ticons,  and  moving-picture  machines,  that  enable  us  to  see 
things  far  away  from,  or  long  after,  their  actual  occurrence. 
All  these  devices  for  enabling  us  to  see  better,  farther,  or  at 
a  different  time  are  called  optical  instruments. 

In  all  of  them  we  find  lenses,  and  in  some  of  them  also 
prisms.  To  understand  how  optical  instruments  work,  we 
must  first  study  the  passage  of  light  through  lenses  and 
prisms;  that  is,  the  refraction  of  light. 

432.  Refraction  in  water.    When  a  stick  stands  obliquely 
in  water,  it  appears  to  be  broken  at  the  surface  of  the  water 
in  such  a  way  that  the  part  under  water  seems  to  be  bent 

427 


428 


PRACTICAL   PHYSICS 


upward  (Fig.  402).     The  bottom  of  a  tank  of  water  always 
appears  to  be  nearer  the  surface  than  it  really  is.     A  fish 

appears  to  be  higher  in  the 
water  than  it  actually  is, 
so  that  if  one  wishes  to 
spear  it,  he  must  aim  under 
its  image.  All  these  phe- 
nomena are  due  to  the  re- 
fraction of  the  light  as  it 
passes  from  water  into  air. 
We  have  said  that  light 

FIG.  402.  — Stick  partly  in  water  appears         j  .  .    T,   -,. 

broken,  advances  in  straight  lines, 

but  this  is  only  true  in  a 

single  substance.     In  general,  when  light  goes  from  one  substance 
into  another  of  different  density,  it  is  bent  or 
refracted  at  the  dividing  surface. 

433.  Law  of  refraction.  To  measure 
how  much  a  beam  of  light  is  bent  in  pass- 
ing from  water  into  air,  we  may  perform 
the  following  experiment. 

We  will  set  a  board 
vertically  in  a  jar  of 
water  and  fasten  a 
wire  of  solder  with 
pins  along  the  board 
(Fig.  403).  If  we  fill 
the  jar  with  water, 

and  then  look  down  along  the  wire,  we  see 
that  the  part  under  water  appears  to  be 
bent  upward.  If  we  bend  the  part  that  is 
out  of  water,  until  the  whole  wire  seems  to 
be  straight,  we  have  a  model  to  show  the 
path  of  the  light  in  air  and  water.  We  may 

now  remove  the  board  from  the  water  and  draw  the  water  line  and  the 

perpendicular  COD  (Fig.  404). 

From  this  experiment  we  see  that  a  beam  of  light  in  pass- 
ing from  water  into  air  is  bent  away  from  the  perpendicular. 


FIG.  403.  —  Light  is  bent 
when  leaving  water 
obliquely. 


FIG.  404. —Diagram    of   ex- 
periment of  figure  403. 


LENSES  AND   OPTICAL  INSTRUMENTS  429 

It  might  also  be  shown  that  a  beam  of  light  in  passing 
from  air  into  water,  in  the  direction  BO,  is  bent  in  the  direc- 
tion OA  (Fig.  404).  That  is,  a  beam  of  light  in  passing 
from  air  into  water  is  bent  toward  the  perpendicular.  In 
this  case  the  line  B  0  represents  the  incident  ray  and  the  line 
OA  the  refracted  ray.  The  angle  (  COB)  between  the  incident 
ray  and  the  normal  is  called  the  angle  of  incidence,  and  the 
angle  ( A  OD)  between  the  refracted  ray  and  the  normal  is 
called  the  angle  of  refraction.  When  light  passes  from  air  into 
water,  the  angle  of  incidence  is  greater  than  the  angle  of 
refraction. 

To  show  the  relation  between  the  angles  of  incidence  and 
refraction,  we  will  lay  off  equal  distances  on  the  incident  and 
refracted  rays  (AO  —  BO),  and  draw  perpendiculars  to  the 
normal  (AD  and  BO).  We  shall  find  that,  whatever  the 
angle  of  incidence,  the  line  BO  is  always  a  definite  number 
of  times  greater  than  AD.  For  example,  in  this  case  BO 
might  be  4  inches,  while  AD  might  be  3  inches,  and  then 
the  ratio  BO/ AD  is  |  or  1.33.  This  ratio  is  called  the  index 
of  refraction.  Experiments  show  that  this  ratio  is  always  the 
same  for  the  same  two  substances,  no  matter  what  the  angle 
of  incidence  may  be. 

This  ratio  may  also  be  expressed  in  terms  of  the  "  sines  "of  the  angles 
of  incidence  and  refraction.  Sine  is  the  name  used  in  trigonometry  for 
the  ratio  of  the  opposite  side  to  the  hypotenuse ;  thus  the  sine  of  the 
angle  of  incidence  (i)  is  BC /BO  and  the  sine  of  the  angle  of  refraction 
(r)  is  AD/AO.  Since  AO  =  BO  by  construction, 

S!neof/*  =  EAC'BO  =  *£  =  index  of  refraction, 
sine  of  Zr     AD/AO     AD 

434.  Refraction  of  light  by  glass.  We  may  also  show  that 
a  beam  of  light  is  refracted  in  passing  from  air  into  glass. 

Let  a  block  of  glass  of  semicircular  shape  be  attached  to  an  optical 
disk,  as  shown  in  figure  405.  It  will  be  seen  that  part  of  the  ray  is  re- 
flected by  the  glass  as  if  it  were  a  mirror,  and  part  is  refracted  as  it 


430 


PRACTICAL  PHYSICS 


passes  into  the  glass.  It  will  also  be  seen  that  the  angle  of  incidence  is 
equal  to  the  angle  of  reflection,  but  is  greater  than  the  angle  of  re- 
fraction. We  may  measure  the  perpendicular  distances  from  the  ends 

of  the  incident  and  refracted  rays  to  the 
normal  00,  and  compute  the  index  of 
refraction  for  glass  and  air. 


Ordinary  crown  glass  bends  a 
ray  of  light  less  —  that  is,  has  a 
smaller  index  of  refraction — than 
glass  made  with  lead,  known  as 
flint  glass.  The  lead  glass,  which 
is  denser,  has  an  index  of  refrac- 
tion with  respect  to  air  of  about 
1.7,  while  that  of  crown  glass 
and  air  is  about  1.5. 


FIG.  405. —  Ray  is  partly  reflected, 
partly  refracted. 


In  general,  light  is  bent  in  passing  obliquely  from  one 
substance  into  another,  as  from  water  to  glass,  diamond  to 
air,  or  even  from  vacuum  to  air  or  from  a  layer  of  air  of  one 
density  to  one  of  another.  Thus  light  is  refracted  in  pass- 
ing through  the  rising  column 
of  warm  air  over  a  stove,  and 
things  seem  to  shimmer  or  dance 
about.  The  general  rule  is  that 
the  lesser  angle  is  in  the  denser 
medium. 

435.  Some  effects  of  refraction. 
An  interesting  case  of  refraction 
of  light  occurs  in  the  atmos- 
phere surrounding  the  earth. 
The  air  extends  only  a  few  miles  above  the  surface  of  the 
earth,  thinning  out  as  it  goes,  and  beyond  is  empty  space. 
So  when  a  ray  of  sunlight  (Fig.  406)  comes  through  ths  air 
obliquely,  it  is  bent  gradually  toward  the  normal  in  passing 
from  one  layer  to  another;  the  result  is  that  the  eye  at  0 
sees  the  sun  in  the  direction  of  the  dotted  line  in  the  figure, 


FIG.  406.  —  Refraction  by  the  earth's 
atmosphere. 


LENSES  AND   OPTICAL  INSTRUMENTS  431 

instead  of  in  its  real  position.  For  this  reason  the  heavenly 
bodies  rise  somewhat  earlier  and  set  somewhat  later  than  they 
would  if  this  were  not  the  case.  This  makes  the  day  some  7 
or  8  minutes  longer. 

436.  Speed  of  light  through  space.  The  reason  for  the 
refraction  of  light  was  not  understood  until  the  velocity  of  light 
in  different  substances  had  been  determined.  Indeed,  up  to 
1675  it  was  believed  that  light  traveled  instantaneously ; 
that  is,  that  light  consumed  no  time  in  its  passage  between 
two  points.  About  that  time  Roemer,  a  young  Danish 


Ez 
FIG.  407.  —  Illustrating  Roemer's  way  of  measuring  speed  of  light. 

astronomer  at  the  Paris  Observatory,  was  observing  the 
moons  of  Jupiter.  With  great  precision  he  observed  just 
when  one  of  the  satellites  M  (Fig.  407)  passed  into  the  shadow 
cast  by  Jupiter,  J.  The  beginnings  of  these  successive 
eclipses  of  Jupiter's  satellite  may  be  thought  of  as  signals 
flashed  at  equal  intervals.  When  the  earth  is  traveling 
away  from  Jupiter,  the  interval  between  signals  is  greater 
than  the  true  interval  because  the  light  from  each  succeed- 
ing signal  has  a  greater  distance  to  travel  to  reach  the  earth. 
But  when  we  are  traveling  toward  Jupiter,  the  interval 
between  signals  is  less  than  the  true  interval,  because  the 
light  from  each  succeeding  signal  has  a  shorter  distance 
to  travel  to  reach  the  earth.  Thus  while  the  earth  is  travel- 
ing from  A  to  B,  the  observed  times  of  the  eclipses  are  delayed 
more  and  more,  and  when  the  earth  has  reached  B,  the  total 


432 


PRACTICAL  PHYSICS 


delay  has  amounted  to  16  minutes  and  36  seconds  (about 
1000  seconds).  This  means  that  it  takes  about  1000  seconds 
for  the  light  to  travel  across  the  earth's  orbit,  a  distance 
of  186,000,000  miles.  Therefore  the  velocity  of  light  is 
186,000  miles  per  second  (300,000  kilometers  per  second).  In 
recent  years  the  velocity  of  light  has  been  directly  measured 
on  the  earth's  surface  by  several  methods,  and  while  the 
measurements  have  been  made  with  great  precision,  the 
results  agree  very  closely  with  those  obtained  so  long  ago  by 
Roemer. 

This  velocity  is  so  enormous  that  it  is  not  strange  that  the 
earlier  experimenters  could  not  determine  it.     In  fact,   it 

takes  only  0.001  of  a  second  for 
light  to  travel  as  far  as  one  can  see 
on  the  earth.  Light  travels  a  very 
little  more  slowly  in  air  than  in  a 
vacuum.  In  denser  substances, 
such  as  water  and  glass,  light 
travels  much  more  slowly. 

437.  Light  waves.  Just  as  we 
think  of  sound  as  transmitted  from 
a  source  through  the  air  by  a  series 
of  waves,  so  we  think  of  light  as 
transmitted  through  space  by  a 
series  of  ether  waves.  When  the 
light  comes  from  a  point  source, 
the  "crest"  or  wave  front  of  a 
wave,  as  it  spreads  in  all  direc- 
tions with  equal  velocity,  is  spherical,  and  the  direction  of 
advance,  being  radial,  is  at  right  angles  to  the  wave  front. 
Figure  408  (a)  represents  such  a  series  of  expanding  waves, 
in  which  the  curved  lines  are  the  wave  fronts  and  the  lines 
of  arrows  indicate  the  direction  of  advance  of  a  small  section 
of  the  wave  front.  These  lines  of  advance  of  light  are  what 
were  called  rays  in  the  last  chapter.  A  bundle  of  light  rays 


FIG.  408.  — Wave  fronts. 


LENSES  AND   OPTICAL  INSTRUMENTS 


433 


is  a  beam.     In  a  "  parallel  beam  "  [Fig.  408  (5)]  the  wave 
fronts  are  plane  and  the  rays  are  parallel. 

By  means  of  a  lens  or  curved  mirror  a  beam  of  light  may 
be  made  to  converge  toward  a  point,  called  the  focus.  In 
this  case  the  wave  fronts  are  concave  spherical  surfaces 
which  contract  as  they  approach  the  focus,  as  shown  in  fig- 
ure 408  0). 

438.  Why  light  is  refracted.     When  a  beam  of  light  passes 
from  air  into  water,  there  is  a  change  in  its  velocity.     To 
see  that  this  must  cause  a  bending 

of  the  beam,  let  the  parallel  lines  in 
figure  409  represent  wave  fronts 
advancing  in  the  direction  of  the 
arrows.  As  soon  as  the  edge  B  of 
a  wave  front  enters  the  water,  it 
begins  to  advance  slowly,  while  the 
part  A,  which  is  still  in  the  air,  ad- 
vances with  the  same  speed  as  be- 
fore. Consequently  the  direction 
of  the  wave  front  is  changed  into 
the  position  CD,  and  the  beam  is 
bent  into  a  direction  nearer  the  per- 
pendicular PR. 

This  is  somewhat  analogous  to  a  column  of  soldiers -march- 
ing from  a  smooth,  hard  field  into  a  rough,  plowed  field, 
where  they  are  slowed  up.  The  man  at  B  hits  the  rough 
ground  before  the  man  at  A  does,  and  so,  while  A  travels 
the  distance  AC,  B  has  gone  a  shorter  distance  BD.  The 
result  is  that  if  B  cannot  hurry,  and  if  A  does  not  slow  up, 
the  column  swings  around  from  its  original  direction  into 
one  nearer  the  perpendicular  PR. 

439.  Speed  of  light  and  index  of  refraction.     From  figure 
409  it  will  be  seen  that  the  amount  which  the  beam  of  light 
is  refracted  when  passing  from  air  into  water  depends  upon 
the  relation  between  the  distances  AC  and  BD\  that  is,  upon 


FIG.  409. 


Refraction  of  oblique 
waves. 


434  PRACTICAL   PHYSICS 

the  relation  between  the  speed  of  light  in  air  and  its  speed 
in  water.  Although  it  is  not  easy  to  measure  the  speed  of 
light  in  water,  yet  it  has  been  done.  The  speed  in  water 
has  thus  been  proved  to  be  about  three  fourths  that  in  air. 
This  means  that  the  speed  of  light  in  air  is  1.33  times  the 
speed  in  water,  which  is  the  same  number  that  we  found  for 
the  index  of  refraction  of  water  and  air.  It  can  be  shown 
that  in  general 

Index  of  refraction--     -?***  in  air 

speed  in  other  substance 

We  may  prove  this  as  follows : 

Index  of  refraction  =  ?HLi  (see  section  433). 
sinr 

But  f  is  equal  to  the  angle  ABC,  and  sin  ABC  =  AC/BC;  also  r  is 
equal  to  the  angle  BCD,  and  sin  BCD  -  BD/BC. 
Therefore, 

srni  =  AC  I  EC  =  AC  =    speed  in  air    =  index  of  refracfcion> 
sin  r     BD/BC      BD      speed  in  water 

440.  Sometimes  no   change  in   direction.     When  a  stick 
stands  vertically  in  water,  it  does  not  appear  to  be  bent, 
because  when  a  beam  of  light  leaves  a  substance  such  as 
water  perpendicular  to  the  surface,  it  suffers  no  refraction. 
The  change  in  velocity  is,  of  course,  just  the  same  whether 
the  light  leaves  the  substance  normally  to  the  surface  or 
obliquely,  but  bending  or  refraction  occurs  only  when  the 
light  leavas  obliquely. 

441.  Total  reflection.     We  have  seen  in  section  432  that 
when  a  beam  of  light  passes  obliquely  from  water  or  glass 
into  air,  the  refracted  ray  is  bent  away  from  the  perpendicu- 
lar.    For  example,  in  figure  410  the  light  coming  from  a 
point  0  under  water,  in  the  direction  oa,  is  refracted  in  the 
direction  aar ;  the  ray  ob  is  refracted  along  W  and  oc  is  re- 
fracted along  cc' .     As  the  angle  in  the  water  increases,  we 
come  finally  to  a  ray  od  which  is  refracted  along  ddf,  and 


LENSES  AND  OPTICAL  INSTRUMENTS 


435 


just  grazes  the  surface  of  the  water, 
formed  between  the  ray  od  and 
the  normal  NM  is  called  the 
Critical  angle.  For  water  and 
air  ifisabout  49°.  If  this  angle 
is  exceeded,  as  in  the  case  of 


The   angle   which   is 


the  ray  oe,  the  ray  cannot  leave  j==£=5f|l 

the  water  at  all,  but  is  totally  : 

reflected  at  e,  just  as  if  it  had 

fallen  on  a  polished  metal  sur-  ^-  -  -#- 

face,  and  takes  the  direction  ee'.   FIG.  410.  —Total  reflection  of  light  by 

The  critical  angle  is  the  angle 

in  the  denser  medium  which  must  not  be  exceeded  if  the  ray  is 

to  get  out. 

To  illustrate  total  re- 
flection, we  may  hold  a 
tumbler  containing 
water  and  a  spoon  above 
the  eye,  and  look  up  at 
the  surface  of  the  water. 
A  very  bright  image  of 
the  part  of  the  spoon  in 
the  water  will  be  seen 

FIG.  411.  -  Refraction  and  reflection  of  light  by  water.    bv  total  reflection . 

If    the    apparatus 

shown  in  figure  411  is  available,  the  paths  of  various  refracted  and  re- 
flected rays,  including  some  that  are  totally  reflected, 
can  be  studied  with  great  ease. 

In  optical  instruments  it  is  frequently 
necessary  to  have  a  very  perfect  reflector, 
and  for  this  purpose  a  right-angle  prism  with 
polished  sides  is  used.  Let  a  ray  of  light 
A  strike  the  side  XZ  of  such  a  prism  (Fig. 
412)  at  right  angles.  It  suffers  no  refrac- 
tion, but  passes  on  through  the  glass  to  B 


FIG.  412. —  Total  re- 
flection of  light  by 
right-angle  prism. 


on  the  side   YZ,  where  it  makes  an  angle  of  45°  with  the 


436 


PRACTICAL  PHYSICS 


n 


normal  mn.  But  the  critical  angle  for  crown  glass  is  about 
42° ;  therefore  the  ray  AB  does  not  emerge  from  the  glass, 
but  is  totally  reflected  in  the  direction  BO.  It  then  strikes 
the  face  XY  perpendicularly  and  emerges  without  refraction. 
The  result  is  that  the  ray  is  bent  90°, 
as  if  there  had  been  a  plane  mirror  at 
TZ. 

442.  Refraction  by  plate  with  paral- 
lel sides.  When  a  ray  of  light  {AB, 
in  figure  413)  passes  through  a  glass 
plate  with  parallel  faces,  such  as  a 
good  window  pane,  it  is  refracted  at  B 
towards  the  normal  N,  and  at  C  away 
from  the  normal  M.  The  result  is 
that  the  ray  CD  is  parallel  to  the  ray 
AB.  Consequently  when  we  look  at 


Fia.  413.  — Path  of  ray 
through  plate  glass. 


any  object  through  a  glass  plate,  we  see  it  slightly  displaced 
in  position,  but  otherwise  unchanged.  When  the  plate  is 
thin,  this  change  of  position  is  too  slight  to  attract  attention. 

443.  Refraction  by  a  prism.  When  a 
ray  XY  enters  one  side  of  a  prism  (yU?<7, 
in  figure  414),  it  is  bent  in  the  direction 
YZ,  and  on  emerging,  it  is  again  bent  in 
the  direction  ZW.  Thus  the  ray  XO  is 
bent  out  of  its  original  course  to  X1W. 
The  total  change  of  direction  is  measured 
by  the  angle  XOX',  called  the  angle  of  de- 
viation. Any  substance  which  has  two 
plane  refracting  surfaces  inclined  to  each  other  is  a  prism. 

The  angle  A  is  called  the  refracting  angle  of  the  prism. 

The  path  of  a  ray  of  light  through  a  prism  can  be  worked 
out  by  drawing  a  diagram,  like  figure  404,  at  iFand  again 
at  Z. 

It  should  be  remembered  that  the  beam  is  always  bent 
toward  the  thicker  part  of  a  prism. 


B  o 

FIG.  414.  —  Refraction 
of  light  by  a  prism. 


LENSES  AND   OPTICAL   INSTRUMENTS 


437 


PROBLEMS 

(The  student  should  have  a  small  protractor.) 

1.  If  the  angle  of  incidence  of  a  ray  of  light  passing  from  air  into 
glass  is  68°,  and  the  angle  of  refraction  is  36°,  find  by  construction  the 
index  of  refraction. 

2.  If  the  index  of  refraction  for  air  and  water  is  1.33,  and  the  larger 
angle  is  60°,  find  by  construction  the  smaller  angle. 

3.  Taking  the  index  of  refraction  as  1.33,  find  by  construction  the 
critical  angle  for  water. 

4.  If  the  critical  angle  for  crown  glass  is  42°,  find  by  construction  the 
index  of  refraction. 

5.  Assuming  the  velocity  of  light  in  air  to  be  about  186,000  miles  per 
second  and  the  index  of  refraction  of  flint  glass  to  be  1.6,  compute  the 
velocity  of  light  in  flint  glass. 

6.  The  angles  of  a  prism  are  20°,  70°,  and  90°.     A  ray  of  light  enters 
normally  the  face  bounded  by  the  angles  90°  and  70°.     The  glass  has  a 
critical  angle  of  42°.     Prove  that  the  ray  will  be  twice  reflected  before  it 
leaves  the  prism. 

444.    Lenses,  convergent  and  divergent.     A  lens  is  a  piece 
of  glass,  or  other  transparent  substance,  with  polished  spher^ 


Double  Conv.ex 


PlcCin 
Convex 


FIG.  415.  —  Converging  lenses. 

ical  surfaces.  A  straight  line  drawn  through  the  centers  Cl 
and  (72  (Fig.  415)  of  the  two  spherical  surfaces  is  called 
the  principal  axis  of  the  lens. 

Lenses  are  divided  into  two  classes,  converging  or  "  thin- 
edged  "  lenses  (Fig.  415),  and  diverging  or  "  thick-edged  " 
lenses  (Fig.  416).  A  converging  lens  is  thinner  at  the  edge 
than  in  the  center.  A  common  type  of  this  class  is  the 


438 


PRACTICAL  PHYSICS 


double  convex  lens.     A  diverging  lens  is  thicker  at  the  edge 
than  at  the  center.     The  double  concave  lens  is  a  common 


Double  Concave 

FIG.  416.  — Diverging  lenses. 


Plane 
Concave 


Diverging 
Meniscus 


lens  of  this  class.     It  should  be  remembered  that  when  a  ray 
of  light  passes  through  a  lens,  it  is  always  bent,  just  as  in  a 

prism,  towards  the  thicker  part 

of  the  lens. 

445.  Action  of  converging 
lens.  Suppose  a  converging  lens  is 
held  so  that  the  sunlight  comes  to  it 
along  its  principal  axis  (Fig.  417). 
The  rays  of  light  will  be  so  re- 
FIG.  417.  —Focus of  convex  leiis.  fracted  as  to  converge  at  a  point  F 

on  the  axis.  If  a  piece  of  paper  is 

held  at  F,  a  small  but  very  bright  image  of  the  sun  is  formed  and  the 

paper  is  quickly  charred.'    The  thicker  the  lens, 

the  nearer  the  point  F  is  to  the  lens,  as  shown 

in  figure  418. 

The  point  F,  where  rays  parallel  to 
the  principal  axis  converge,  is  called 
the  principal  focus  of  the  lens.  The  dis- 
tance from  the  lens  to  the  principal  focus 
is  called  the  focal  length,  /,  of  the  lens. 

Since  an  incident  ray  and  its  corre-   FIG.  418. —  Focal  length  of 

*  thick  and  thin  lenses. 

sponding  refracted  ray  are  reversible,  it 

follows  that  a  light,  placed  at  the  principal  focus  F,  would 

send  its  rays  through  the  lens  in  such  a  way  as  to  come  out 

parallel. 


LENSES  AND   OPTICAL  INSTRUMENTS  439 

446.  How  a  lens  is  made.     The  surface  of  a  lens  is  shaped 
by  grinding  together  the  glass  and  an  iron  matrix  with  every 
possible  variety  of  sliding  motion.     The  glass  and  the  matrix 
are  thus  brought  automatically  to  an  almost  perfect  spher- 
ical shape.     The  polishing  is  done  by  using  finer  and  finer 
grinding  materials  in  succession  (usually  powdered  emery  or 
carborundum),  ending  with  rouge.     In  the  later  stages  the 
matrix  is  lined  with  a  layer  of  stiff  pitch  with  cross  grooves 
cut  in  its  surfaces  to  hold  the  rouge. 

447.  Conjugate  foci.     When  the  light  from  an  object  0  on 
the  principal  axis  passes  through  a  double  convex  lens,  the 
rays,    after    leaving    the 

glass,  converge  at  a  point 

I.     Two  such   points,    0 

and  7,  are  called  conjugate 

foci,  for  if  the  object  were  z)Qoo 

placed    at    J,    the    image     FIG. 1u9.- image  of  distant  object  is  at  *\ 

would   be    at    0.     If   the 

point  0  is  not  on  the  principal  axis,  the  line  joining  0  and  1 

passes  through  the  center  of  the  lens,  called  its  optical  center, 

and  the  line  is  called  a  secondary  axis. 

When  the  lens  is  thin,  the  same  formula  holds  as  was  used 
for  mirrors  (section  430). 

-L+l  =1 
i>o    A   / 

where  D0  =  distance  of  object  from  lens, 
Dj=  distance  of  image  from  lens, 
f=  focal  length  of  lens. 

448.  Discussion  of  the  lens  formula.     If  the  object  is  so  far 
away  that  the  rays  from  any  point  of  it  to  different  parts  of 
the  lens  are  practically  parallel,  the  image  is  formed  at  F '; 

for  D0  is  very  large,  and  so  —  is  nearly  zero;  this  leads  to 

™o 
DI=f,  as  shown  in  figure  419. 


440 


PRACTICAL  PHYSICS 


If  the  object  is  brought  nearer  the  lens,  the  image  moves 
farther  away  from  the  lens.  When  D0  =  2/,  D7=  2/also, 
as  shown  in  figure  420. 


•-Do=2f 
FIG.  420.  —  Image  at  same  distance  as  object. 


Do=f 


FIG.  421.  —  Object  at  F,  rays  emerge 
parallel. 


If  the  object  is  brought  still  nearer  the  lens,  the  image 

moves   still   farther   away   from    the   lens,  until,  when   the 

object  is  at  the  principal  focus  F, 
the  distance  of  the  image  becomes 
infinitely  great,  and  the  rays  that 
go  out  from  the  lens  are  parallel, 
as  shown  in  figure  42?1. 

If  the  object  is  brought  even 
nearer  the  lens,  the  rays  on  the 

farther  side  diverge  as  if  they  came  from  a  focus  I  behind 

the  lens  (Fig.  422).     In  this  case,  the  formula  shows  that  D/is 

negative.     This    means    that 

the  image  is  behind  the  lens. 
For   divergent   lensesr  the 

same  formula  can  be  used,  if 

the  focal  length  f  is  regarded 

as  negative. 

449.     Images    formed    by      FlG-  422-  ~ Object  inside  F,  image  vir- 

lenses.     The    geometrical 

construction  of  images  formed  by  lenses  will  indicate  the  size 
and  position  of  these  images.  The  method  of  procedure  is 
the  same  as  that  used  for  spherical  mirrors  (section  425).  If 
we  trace  two  rays  from  any  point  of  the  object  to  their 
intersection,  we  have  the  position  of  the  corresponding  point 
of  the  image.  For  example,  in  figure  423,  a  ray  from  A 
parallel  to  the  principal  axis  must,  after  refraction  by  the 


LENSES  AND  OPTICAL  INSTRUMENTS 


441 


lens,  pass  through  the 
principal  focus  F.  An- 
other ray  from  A,  passing 
through  the  center  of 
lens,  is  undeviated.  The 
point  A1  where  these  rays 
meet  is  the  image  point 
of  A.  Then  from  similar  triangles  it  is  readily  seen  that 


FIG.  423.  —  Size  of  real  image. 


Length  of  image  _  distance  of  image  from  lens 
Length  of  object     distance  of  object  from  lens 

The  ratio  of  the  length  of  the  image  to  the  length  of  the 
object  is  called  the  linear  magnification. 

In  figure  423  the  object  AB  was  beyond  the  principal  focus  of 
"••.0,^.  A'  ^ne  convex  lens, 

'^--^  Le^s  and    the    image 

A'B1  is  inverted, 
real,  and  in  this 
case  smaller  than 
the  object. 

In  figure  424 
the  object  AB  is 
between  the  prin- 
cipal   focus    F 
virtual,    and   larger, 


Lens 


,--?'   Virtual  Image 

FIG.  424.  —  Size  of  virtual  image. 

and  the  lens.     The   image   A'B1  is   erect, 

and  can  only   be  seen  by  looking  through  the  lens. 

In  figure  425  the  lens  is  concave 
and  the  image  is  erect,  virtual,  and 
smaller. 

In  all  these  cases  it  will  be  seen 
that  straight  lines  drawn  from  the 
extremities  of  the  object  through 
the  center  of  the  lens  pass  through 
the  extremities  of  the  image,  and 

FIG.  425.  — Virtual  image  formed 

therefore  the  diameters  or  lengths  by  concave  lens. 


442  PRACTICAL  PHYSICS 

of  object  and  image  are  to  each  other  as  their  respective  dis< 
tances  from  the  center  of  the  lens,  as  stated  in  the  formula 
above. 

450.  Defects  of  images  formed  by  lenses.  In  figure  423  it 
was  assumed  that  the  real  image  A' B1  was  a  straight  line. 
But  it  will  be  seen  that  the  point  A  of  the  object  is  at  a 
greater  distance  from  the  center  of  the  lens  0  than  the 
point  B,  and,  therefore,  according  to  the  lens  equation,  Bf 
ought  to  be  farther  from  the  center  of  the  lens  than  A'.  In 
other  words,  the  image  is  curved.  This  means  that  if  a  cam- 
era is  equipped  with  a  simple  convex  lens,  and  the  center 
of  the  plate  is  sharply  focused,  the  edges  will  be  fuzzy,  since 
the  image  does  not  lie  in  one  plane.  This  is  especially  notice- 
able for  a  large  object  comparatively  close  to  the  lens. 

In  the  construction  of  figure  423  it  was  assumed  that  all 
the  rays  coming  from  a  point  in  the  object  are  accurately  re- 
fracted by  the  lens  to  one  point.  But  as  a  matter  of  fact  the 
rays  that  strike  the  outer  portions  of  a  lens  are  refracted 
more  strongly  than  the  rays  which  fall  on  the  central  portion 
of  the  lens,  and  so  come  to  a  focus  nearer  to  the  lens.  This 
lack  of  exact  concurrence  is  called  spherical  aberration. 

The  effects  of  spherical  aberration  are  to  make  the  image 
indistinct  and  to  distort  its  shape.  If  the  outer  rays  are 
cut  out  by  means  of  a  diaphragm  or  stop,  the  sharpness  of  the 
image  is  improved,  but  at  the  same  time  its  brightness  is 
diminished.  In  large  lenses,  such  as  those  used  in  telescopes, 
the  outer  portions  are  so  ground  that  their  refracting  power 
is  diminished  by  the  proper  amount  to  insure  distinct  images. 

This  whole  geometrical  theory  of  lenses  applies  only  to 
very  thin  lenses,  and  to  cases  where  the  light  may  be  assumed 
to  pass  through  the  lens  in  a  direction  not  greatly  inclined  to 
the  axis  of  the  lens.  In  practice,  combinations  of  lenses  are 
nearly  always  used  instead  of  simple  lenses,  and  these  com- 
binations are  designed  so  that  the  imperfections  of  one  lens  are 
compensated  or  balanced  by  the  imperfections  of  another  lens. 


LENSES  AND   OPTICAL  INSTRUMENTS 


443 


PROBLEMS 

1.  A  convex  lens  has  a  focal  length  of  16  centimeters.     Find  the  posi- 
tion and  nature  of  the  images  formed  when  objects  are  placed  10  meters, 
50  centimeters,  and  10  centimeters  respectively  from  the  lens. 

2.  If  an  object  is  placed  32  centimeters  from  the  lens  described  in 
problem  1,  how  far  is  the  image  from  the  lens? 

3.  A  lamp  placed  60  centimeters  from  a  lens  forms  a  distinct  image  on 
a  screen  20  centimeters  away  on  the  other  side.     Find  the  focal  length  of 
the  lens. 

OPTICAL  INSTRUMENTS 

451.    Photographic  camera.     The  simplest  form  of  camera 

consists  of  a  light-tight  box  (Fig.  426)  with  a  converging  lens 

at  one  end,  so  mounted  as  to  form 

an  image  of  an  outside  object  upon 

a  sensitive  plate.     This  plate  consists 

of  a  silver  compound  spread  on  a 

glass  plate  or  celluloid  sheet  (film). 

The  light  is  allowed  to  pass  through 

the   lens  for   a   time  which  varies 

from  a  thousandth  of  a  second  up 

to  several  minutes,  according  to  the 

lens,  the  brightness  of  the  object  to  be  photographed,  and  the 
"  speed"  of  the  sensitive  plate.  The  image 
on  the  plate  is  not  visible  until  the  plate  is 
placed  in  a  mixture  of  chemicals  called  a 
"developer."  To  obviate  the  spherical 
aberration  of  a  single  lens  a  diaphragm  is 
put  in  front  of  the  lens  so  as  to  limit  the 
size  of  the  pencil  of  light.  With  a  small 
opening,  or  "  stop,"  we  get  great  sharpness 
in  the  picture,  but  must  expose  it  for  a 
longer  time.  A  "  combination  lens,"  with 
the  diaphragm  between  the  two  lenses 
(Fig.  427),  is  used  to  take  clear  pictures 


FIG.  426.  —  A  simple  camera. 


Fia.  427.  —  Combina- 
tion lens  for  rapid 
work. 


444 


PRACTICAL  PHYSICS 


FIG.  428.  —  Projecting  lantern. 


of  a  rapidly  moving  object.     Since  the  plate  on  which  the 

image  is  formed  must  be  in  the  position  which  is  the  conjugate 

focus  of  the  position  occupied  by  the  object,  the  camera  is 

usually  made  with  a 
bellows  so  that  it  can 
be  "  focused "  on  ob- 
jects at  varying  dis- 
tances. 

452.  Projecting  lan- 
tern. The  projecting 
lantern,  or  stereopticon, 
"si  is  used  to  throw  an 
image  of  a  brilliantly 
illuminated  object  or 
picture  upon  a  screen. 
It  consists  essentially 

of  a  powerful  source  of  light,  such  as  an  electric  arc  A  (Fig.  428), 

the  condensing  lenses  (7,  which  converge  the  light  through  the 

slide  or  transparent  picture  &,  and   the  front  lens  or  objective 

Z,  which  forms  a  real  image  of  the  picture  on  the  screen  Sr. 

It  will  be  noticed  that  the  lantern  is  much  like  the  camera 

except  that  the  object  and  image 

have  been  interchanged.     Since  the 

screen  is  usually  at  a  considerable 

distance,  the  slide  $  is  only  a  little 

beyond  the  principal  focus  of  the 

objective  L.     It  is  very  important 

to    have    a    powerful    light    source 

which  is  small   in    size.     For   this 

purpose  electric  arcs,  calcium  lights, 

acetylene  lights,  and  electric  glow 

lamps,  in  which  the  filament  is  coiled 

into  a  small  space,  are  sometimes 

used.     Figure  429  shows  the  arrangement  of  the  lantern  to 

project  opaque  pictures,  such  as  post  cards. 


FIG.  429.  —  Projection  of  opaque 
objects. 


LENSES  AND   OPTICAL  INSTRUMENTS  445 

The  moving-picture  machine,  which  is  now  so  common,  is  a 
projecting  lantern  designed  to  show  lifelike  motion.  A 
series  of  photographs  is  taken  with  a  camera  provided  with 
a  shutter  which  automatically  opens  and  shuts  about  12  times 
a  second.  A  long  narrow  film  moves  a  little  while  the 
shutter  is  closed,  but  remains  stationary  while  it  is  open. 
Each  of  such  a  series  of  pictures  differs  slightly  from  the 
preceding  one,  if  anything  is  moving  in  the  field  of  the 
camera. 

Then  this  series  of  pictures  is  thrown  on  the  screen  at  the 
same  rate  as  that  at  which  they  were  taken.  The  sensation 
produced  by  one  picture  re- 
mains until  the  next  picture 
appears,  so  that  we  are  not 
aware  of  any  interruption  be- 
tween the  pictures. 

453.  The  eye.  The  human 
eye  (Fig-  430)  is  essentially 
a  little  camera,  with  a  lens 
system  in  front,  and  a  sensi- 
tive  film,  made  of  nerve  fibers, 

.  i      i       i  FIG.  430.  —  Section  of  the  human  eye. 

at  the  back. 

It  has  the  great  advantage  over  any  other  camera  in  that 
it  can  take  a  continual  succession  of  pictures  all  on  the  same 
film,  '"  developing "  them  by  some  unknown  chemical  or 
electrical  process  in  the  nerve  fibers  instantaneously,  and 
transmitting  the  results  equally  instantaneously  over  a 
"  private  wire "  (the  optic  nerve)  to  "  headquarters "  (the 
brain). 

The  structure  of  the  eye  is  shown  in  figure  430.  There 
is  an  outer  horny  membrane,  the  cornea,  holding  a  watery 
fluid  called  the  aqueous  humor.  There  are  also  an  adjustable 
diaphragm,  or  "  stop,''  called  the  iris,  and  a  crystalline  lens. 
The  latter  is  of  somewhat  higher  index  of  refraction  than 
either  the  aqueous  humor  in  front  or  a  similar  fluid,  the  vitre- 


446  PRACTICAL  PHYSICS 

ous  humor,  behind.     At  the  back  is  the  nerve  layer  or  retina, 
which  acts  as  the  sensitive  film. 

It  should  be  noticed  that  most  of  the  converging  power 
of  the  eye  comes,  not  in  the  lens,  but  at  the  front  surface  of 
the  cornea.  This  explains  why  we  can  never  see  objects 
distinctly  when  swimming  under  water.  The  aqueous  fluid 
and  the  water  outside  are  so  much  alike  that  there  is  no 
longer  any  refraction  of  the  light  as  it  strikes  the  cornea, 
and  the  lens  by  itself  is  not  powerful  enough  to  bring  the 
light  to  a  sharp  focus  on  the  retina. 

454.  Focusing  the  eye.     If  an  object  is  moved  nearer  a 
camera,  the  distance  between  the  plate  and  lens   must   be 
increased,   or  else  a  lens  of  greater  convexity,  that  is,  of 
shorter  focus,  must  be  substituted,  if   the  picture  is  to  be 
sharp.     Of  these  two  possibilities,  the  eye  chooses  the  sec- 
ond.    It  adapts  itself  to  varying  distances,  not  by  moving 
the  retina,  but   by  changing   the   focal  length  of   the  lens. 
When  the  muscles  of  the  eye  are  relaxed,  the  lens  is  usually 
of  such  a  shape  as  to  focus  clearly  on  the  retina  objects 
which  are  at  a  considerable  distance.     When  one  wishes  to 
look  at  near  objects,  a  ring  of  muscle  around  the  crystalline 
lens  causes  the  lens  to  become  more  convex,  so  as  to  form 
a  distinct  image  on  the  retina.     It  is  often  said  that  objects 
are  seen   most    distinctly  when   held   about   10    inches  (25 
centimeters)  from   the   eye.      This   simply  means   that  10 
inches  is  about  as  near  as  one  can  usually  focus  an  object 
distinctly,  and  since  the  shortest  distance  gives  the  largest 
image,  this  is  where  we  automatically  hold  an  object  when 
we  want  to  see  its  details. 

455.  Imperfections   of  the   eye.      In  the    short-sighted  eye 
the  image  of  a  distant  object  is  formed  in  front  of  the  retina 
(at  A,  in  figure  431).      This  may  be  due  to  too  great  con- 
vexity in  the  crystalline  lens,  or  to  the  oval  shape  of  the  eye- 
ball.    A   person  who    is  short-sighted  must  bring  objects 
close  to  the  eye  to  see  them  distinctly. 


LENSES  AND   OPTICAL  INSTRUMENTS 


447 


In  the  far-sighted  eye  the  image  of  an  object  at  an  ordinary 
distance  would  be  formed  behind  the  retina  (at  B,  in  figure 
432).  This  is  because  the  crystalline  lens  is  too  flat,  or  the 


FIG.  431.  —  Short-sighted  eye. 


FIG.  432.  —  Far-sighted  eye. 


length  of  the  eyeball  is  too  short.     To  see  distinctly,  such  a 
person  must  hold  objects  at  a  distance. 

Spectacles  with  concave  lenses  are  used  to  correct  short-sighted 
eyes,  and  convex  lenses  are  used  for  far-sighted  eyes. 

Another  defect  of  the  eye  is  astig- 
matism, which  occurs  when  the  leris  of 
the  eye,  or  the  cornea,  does  not  have 
truly  spherical  surfaces.  The  effect  is 
that  a  spot  of  light,  like  a  star,  is  seen 
as  a  short,  bright  line.  In  a  case  of 
astigmatism  all  the  lines  in  such  a 
diagram  as  figure  433  will  not  appear 
equally  distinct.  Those  in  one  direc- 
tion will  be  sharply  defined,  while  FIG.  433.  —  Lines  to  test  as- 
those  at  right  angles  to  them  will  ap- 
pear broadened  and  blurred.  This  defect  is  corrected  by  the 
use  of  cylindrical  lenses. 

456.   Apparent  distance  and  size.      The  apparent  size  of  an 

object  depends  on  the  size  of  the 
image  formed  on  the  retina,  and 
consequently  on  the  visual  angle. 
From  figure  434  it  is  evident 
that  this  angle  increases  as  the 
object  is  brought  nearer  the  eye. 


FIG.  434.  —  The  visual  angle. 


For  example,  when  we  look  along   a  railroad  track,  the 
rails  seem  to  come  nearer  together  as  their  distance  from  us 


448  PRACTICAL   PHYSICS 

increases.  The  image  of  a  man  100  yards  away  is  one  tenth 
as  large  as  the  image  of  the  same  man  when  he  is  10  yards 
off.  We  do  not  actually  interpret  the  larger  image  and 
larger  visual  angle  as  meaning  a  larger  man,  because  by  ex- 
perience we  have  learned  to  take  into  account  the  known 
distance  of  an  object  in  estimating  its  size. 

Distant  objects  seen  in  clear  mountain  air  often  seem 
nearer  than  they  really  are.  This  is  because  we  see  the  ob- 
jects more  clearly  and  distinguish  the  details  more  sharply; 
and  this  often  leads  us  to  think  that  they  are  smaller  than 
they  really  are.  The  moon,  on  the  other  hand,  seems  bigger 
when  near  the  horizon,  because  we  can  compare  it  with  ob- 
jects whose  size  we  know.  It  is  only  by  long  experience  that 
we  learn  to  estimate  the  actual  size  and  distance  of  objects. 
457.  The  simple  microscope  or  magnifying  glass.  We 
have  said,  in  section  454,  that  the  distance  of  most  distinct 
vision  is  about  10  inches.  If  an  object  is  placed  at  a  greater 
distance  than  this,  the  image  on  the  retina  is  smaller  and 
the  details  of  the  object  are  not  seen  so  distinctly.  If  the 

object  is  placed  nearer  than 
_...— .^-"^  this,  the  image  on  the  retina 

is  blurred.  When  an  object 
is  examined  by  a  magnifying 
glass,  the  distance  between  the 
lens  and  the  object  is  made 

less   than   the    focal    length, 
FIG.  435.  —  Magnifying  glass.  ^  -, .  j      ,  i 

and     so     adjusted    that    an 

erect  enlarged  virtual  image  is  formed  about  10  inches  away 
(Fig.  435).  The  magnifying  power  of  a  simple  microscope 
is  the  ratio  of  the  size  of  the  image  to  the  size  of  the  object. 
This  is  equal  to  the  distance  of  the  image  divided  by  the  dis- 
tance of  the  object,  that  is,  10/Z>0,  D0  being  the  distance  of 
the  object  (in  inches)  from  the  lens. 

Thus  if  a  magnifying  glass  can  be  held  1  inch  from  an 
insect,  the  magnification  will  be  10  diameters. 


LENSES  AND   OPTICAL  INSTRUMENTS 


449 


458.  Compound  microscope.  Very  small  objects  are  made 
visible  by  the  compound  microscope.  It  consists  of  two  lenses 
or  lens  systems  which  are  placed  at  the  ends  of  a  tube.  The 
object  AB  is  put  just  outside  the  principal  focus  of  the 
smaller  lens  L  (Fig.  436),  called  the  objective,  which  forms 
an  enlarged,  real  image  CD.  This  real  image  is  then  ex- 


FIG.  436.  —  Compound  microscope. 

amined  through  the  eyepiece  E,  which  acts  like  a  magnifying 
glass,  giving  a  still  larger  virtual  image  at  C'D',  about  10 
inches  from  the  eye. 

The  image  CD  is  magnified  as  many  times  as  its  distance 
from  the  lens  L  is  greater  than  the  focal  length  of  that  lens. 
Usually  the  distance  of  CD  from  L  is  about  150  millimeters, 
and  so,  if  the  lens  has  a  focal  length  of  5  millimeters,  the 


450 


PRACTICAL  PHYSICS 


image  CD  is  30  times  as  long  as  the  object  AB.  If  the  eye- 
piece still  further  magnifies  the  image  10  times,  the  magni- 
fying power  of  the  combination  is  10  x  30,  or  300  diameters. 
Microscopes  which  magnify  as  much  as  2500  diameters  are 
sometimes  used. 

We  are  indebted  to  the  microscope  for  many  of  our  most 
valuable  discoveries  about  the  structure  and  life  of  plants 
and  animals,  about  the  smallest  living  things,  and  about  the 
causes  of  disease. 

459.  The  telescope.  The  telescope  enables  us  to  see  clearly 
objects  so  far  away  that  we  could  not  otherwise  see  their 


Fia.  437.  —  Astronomical  telescope. 

details.  The  simpler  sort,  called  the  astronomical  telescope, 
consists  of  two  lenses  or  lens  systems,  the  large  objective  0 
(Fig.  437)  and  the  eyepiece  E.  The  inverted  real  image 
J,  formed  by  the  lens  0,  is  much  smaller  than  the  object, 
but  it  is  brought  so  near  to  the  observer  that  it  can  be  exam- 
ined through  the  eyepiece  E,  which  acts  like  a  magnifying 
glass.  The  two  lenses  are  mounted  in  an  extension  tube  so 
that  the  eyepiece  can  be  drawn  farther  from  the  objective 
when  objects  near  at  hand  are  to  be  examined.  Since  the 
magnifying  glass  or  eyepiece  (Joes  not  reinvert,  the  observer 
sees  things  upside  down,  just  as  he  does  in  a  microscope. 


LENSES  AND   OPTICAL   INSTRUMENTS 


451 


It  can  be  shown  that  the  magnifying  power  of  an  astronomi- 
cal telescope  is  equal  to  the  number  of  times  the  focal  length  of 
the  eyepiece  is  contained  in  the  focal  length  of  the  object  glass. 

460.  The  erecting  telescope  or  spyglass.  This  instrument 
(Fig.  438 )  is  like  the  astronomical  telescope  except  that  an 
additional  converging  lens  or  lens  system  L  is  introduced 
between  the  object  glass  0  and  the  eyepiece  E.  This  lens 
L  inverts  the  image  T,  forming  another  real  image  at  I1 ; 


FIG.  438.  —  Erecting  telescope  or  spyglass. 

then  this  erect  image  I'  is  magnified  by  the  eyepiece,  which 
forms  an  enlarged,  erect,  virtual  image  I".  In  the  ordinary 
spyglass  the  eyepiece  is  a  combination  of  two  lenses,  which 
act  like  a  single  magnifying  glass.  The  introduction  of  the 
erecting  lens  L  lengthens  the  telescope  tube  considerably. 

461.  Telescope  used  for  sighting.  A  gun  cannot  be 
sighted  with  the  greatest  possible  accuracy  if  its  sights  are 
pins  or  pointed  projections.  This  is  because  it  is  impossible 
to  focus  the  eye  both  on  the  sights  and  on  a  distant  object 
at  the  same  time.  For  example,  the  best  that  can  be  done 
with  the  naked  eye  at  a  distance  of  100  yards  is  subject  to 
error  of  one  or  two  inches.  Therefore  many  of  the  best  long- 
range  rifles  are  provided  with  telescopic  sights.  Similarly, 
surveyors  make  use  of  the  telescope  in  their  "  transits  "  and 


452 


PRACTICAL  PHYSICS 


FIG.  439.  —  Surveyor's  level. 


"levels."  In  all  such  cases  two  very  fine  wires  or  spider 
lines  are  stretched  across  the  telescope  in  the  plane  where 
the  image  of  the  distant  object  is  formed  by  the  object  glass, 

and  the  intersection  of  these 
two  cross  hairs  is  made  to 
coincide  with  the  image  of 
any  given  point  of  the  object. 
When  this  adjustment  is 
made,  a  line  drawn  from  the 
point  of  intersection  of  the 
cross  hairs  through  the  center 
of  the  object  glass  passes 
through  the  given  point  of 
the  object. 

462.  The  opera  glass  and  field  glass.     The  opera  glass  (Fig. 
440)  is  a  telescope  whose  eyepiece  is  a  di- 
verging or  concave  lens.     Since  the  eye- 

piece  has  approximately  the  same  focal 
length  as  the  eye  of  the  observer,  its  effect 
is  practipally  to  neutralize  the  lens  of  the 
eye.  So  we  may  consider  that  the  object 
glass  forms  its  image  directly  on  the  ret- 
ina. The  field  of  view  of  the  opera  glass 
is  small,  and  so  the  opera  glass  is  usually 
made  to  magnify  only  three  or  four  times. 
But  it  has  the  advantage  of  being  compact 
and  gives  an  erect  image.  Galileo  made 
a  telescope  on  this  plan  which  magnified 
about  30  diameters  and  enabled  him  to 
make  some  exceedingly  important  dis- 
coveries. A  large-sized  opera  glass  is 
usually  called  a  field  glass. 

463.  The  prism  field  glass  or  binocular. 
An  instrument,  called  a  binocular,  has  come 

into  use  in  recent  years  which  has  the  wide    FIG.  440.— Opera  glass 


PUPIL  OF   EYE 
LENS  OF   EYE 


LENSES  AND   OPTICAL  INSTRUMENTS 


453 


FIG.  441.  — Prism  binocular. 


field  of  view  of  the  spyglass  and  at  the  same  time  the  com- 
pactness of  the  opera  glass.  This  compactness  is  obtained  by 
causing  the  light  to  pass  back  and  forth  between  two  reflect- 
ing prisms,  as  shown  in  figure  441.  This  device  enables  the 
focal  length  of  the  object  glass  to  be  three  times  as  great  as 
in  the  ordinary  field 
glass  for  the  same 
length  of  tube,  and 
so  the  magnifying 
power  is  correspond- 
ingly increased. 

Furthermore,  the 
reflections  in  the 
two  prisms  secure 
an  erect  image  with- 
out using  the  erect- 
ing lens  of  the  ordinary  terrestrial  telescope;  for  one  double 
reflection  tips  the  image  right  side  up,  and  the  other  shifts 
right  and  left,  thus  restoring  it  completely  to  its  natural 
position. 

PROBLEMS 

1.  When  a  camera  is  focused  on  an  automobile  100  yards  away,  the 
plate  is  8  inches  from  the  lens.     How  much  must  the  distance  between 
the  lens  and  the  plate  be  changed  when  the  automobile  is  only  10  yards 
away?    Must  the  distance  be  shortened  or  lengthened? 

2.  A  5  inch  post  card  is  to  be  projected  on  a  screen  20  feet  away  so 
as  to  be  5  feet  long.     Find  the  focal  length  of  the  lens  required. 

3.  A  photographer  with  a  "  12  inch  lens  "  wants  to  make  a  full-length 
picture  of  a  6  foot  man  standing  10  feet  from  the  lens.     How  near  the 
lens  must  the  plate  be  placed  ? 

4.  How  long  a  plate  must  be  used  in  problem  3  ? 

5.  How  near  to  an  object  must  a  hand  magnifier  of  1.2  inches  focal 
length  be  held  to  magnify  it  6  diameters? 

6.  A  reading  glass  of  5  inches  focal  length  is  held  4  inches  from  a 
printed  page.     How  much  does  it  magnify? 

7.  It  is  necessary  to  project  a  slide  3  inches  wide  on  a  wall  40  feet 


454  PRACTICAL  PHYSICS 

distant,  so  that  the  picture  shall  be  10  feet  wide.     What  must  be  the 
focal  length  of  the  objective  of  the  lantern  ? 

8.  In  a  compound  microscope  the  objective  lens  L  (Fig.  436)  has  a 
focal  length  of  one  inch  and  the  object  AB  is  1.1  inches  away.    How  far 
from  the  lens  is  the  image  CZ>?     How  many  times  is  it  magnified?     If 
the  eyepiece  magnifies  this  image  20  times,  what  is  the   magnifying 
power  of  the  instrument  ? 

9.  A  telescope  has  an  objective  whose  focal  length  is  30  feet,  and  an 
eyepiece  whose  focal  length  is  1  inch.      How  many  diameters  does  it 
magnify  ? 

10.  The  focal  length  of  the  great  lens  at  the  Yerkes  Observatory  is 
about  60  feet  and  its  diameter  40  inches.  The  eyepiece  has  a  focal 
length  of  0.25  inches.  Calculate  its  magnifying  power. 


SUMMARY   OF   PRINCIPLES   IN    CHAPTER    XXII 

Refraction  occurs  when  light  passes  obliquely  from  one  substance 
to  another. 

Smaller  angle  is  always  in  denser  medium. 

sine  of  larger  angle 

Index  of  refraction  =  -  —  > 

sine  of  smaller  angle 

speed  in  rarer  medium 
speed  in  denser  medium 

Velocity  of  light  =  186,000  miles  per  second, 

=  3  X  1010  centimeters  per  second. 

Critical  angle  is  smaller  angle,  when  larger  angle  is  90°. 

Prism  bends  light  toward  thick  edge. 
Convergent  (thin  edged)  lens  bends  light  inward. 
Divergent  (thick  edged)  lens  bends  light  outward. 

Principal  focus  denned  as  convergence  point  for  rays  parallel  to 
axis. 

Lens  formula:  Holds  for  both  converging  and  diverging  lenses:  — 


Object  distance      image  distance      focal  length 


LENSES  AND   OPTICAL  INSTRUMENTS 


455 


For  convergent  lens,  focal  length  is  positive. 
For  divergent  lens,  focal  length  is  negative. 
For  real  image,  beyond  lens  from  object,  image  distance 

comes  out  positive. 
For  virtual  image,  on  same  side  of  lens  as  object,  image 

distance  comes  out  negative. 

Size  rule :  Holds  for  both  converging  and  diverging  lenses :  — • 

Length  of  image  _  image  distance 
Length  of  object      object  distance 

QUESTIONS 

1.  Which  people   would  be  likely  to  become   short-sighted  early, 
those  who  live  much  out  of  doors  or  those  who  stay  much  indoors? 

2.  Compare  the  eye,  part  by  part,  with  the  camera. 

3.  How  does  a  "  wide-angle  "  lens  differ  from  a  long- 
focus  lens? 

4.  What  are  the  defects  of  a  pinhole  camera  ? 

5.  What  is  the  difference  between  a  refracting  and 
a  reflecting  telescope  ? 

6.  Prism  glass,  with  a  section  like  that  shown   in 
figure  442,  is  often  used  for  the  upper  part  of  shop  windows 
and  doors  and  for  windows  facing  on  narrow  courts.  Why? 

7.  Why  is  it  necessary  to  build  powerful  telescopes 
very  wide  as  well  as  very  long  ? 

8.  Why  must  a  compound  microscope  be  so  accu- 
rately focused  on  the  object? 

9.  Why  is  it  best  to  have  your  light  for  writing  or 
sewing  come  from  over  your  left  shoulder? 

10.  Explain  how  the  wheels  of  moving  vehicles  in  a 
moving  picture  sometimes  seem  to  be  rotating  backwards. 

11.  What  part  do  the  condensing  lenses  play  in  the       ttoaofplmteol 
action  of  a  stereopticon  ?  prism  glass. 


CHAPTER   XXIII 


SPECTRA  AND   COLOR 

Prism  spectrum  —  achromatic  lenses — spectroscope  —  types 
of  spectra  —  spectrum  analysis  —  Fraunhofer  lines  —  wave  length 
of  light  —  colors  of  objects  —  colors  of  thin  films  —  infra-red 
and  ultra-violet  —  electromagnetic  theory. 

464.   Analysis  of  light  by  prism.  If  we  let  a  beam  of  sunlight  pass 
through  a  narrow  slit  into  a  dark  room,  and  put  a  glass  prism  in  its  path 
(Fig.  443),  the  beam  of  light  is 
refracted.     If    we    put    a    white 
screen  in   the    path   of    the  re- 
fracted light,  a  band  of  colors  is 
formed.      In  this  band  are  red, 
yellow,   green,   blue,  and  violet, 
though  there  are  no  sharp  lines 
of  division  between  them. 

This  colored  band,  which 
shades  off  gradually  from 
red  to  violet,  is  called  a 
spectrum.  This  shows  that 

the  ordinary  white  light  of  the  sun  is  complex  and  contains 
different  kinds  of  light.  The  light  which  is  refracted  least, 
the  eye  recognizes  as  red,  and  that  which  is  most  refracted, 
as  violet.  It  will  be  shown  later  that  the  physical  property  of 
light  which  determines  this  difference  in  refrangibility  is  the 
wave  length. 

To  show  that  the  prism  itself  did  not  produce  the  different 
colors,  but  simply  separated  various  kinds  of  light  already 
present  in  the  beam  of  sunlight,  Sir  Isaac  Newton  placed  a 
second  prism  in  the  spectrum,  so  that  only  violet  light  fell 
on  it.  He  found  that  the  violet  light  was  again  refracted, 
but  that  there  was  no  further  change  in  color. 

456 


FIG.  443.  —  Light  decomposed  by  prism. 


SPECTRA   AND   COLOR 


457 


He  also  found  that  when  these  dispersed  or  spread  out, 
colored  lights  were  brought  together  by  a  converging  lens 
(Fig.  444),  white  light  was 
the  result. 

465.  Achromatic    lenses. 
When       sunlight       passes 
through  an  ordinary  double 

convex  lens  made  of  a  single  FlG  ^_Com]iinins  spectral  colors  into 
piece  of  glass,  the  light  is  white  light, 

refracted  and  converges  at 

a  point  called  the  focus.  But  the  light  is  also  dispersed, 
just  as  in  a  prism,  and  the  focus  for  red  light  (72,  in  figure 
445)  is  at  a  greater  distance  from  the  lens  than  that  for 

violet  light  (F).  Such  a 
single  lens  cannot  give  a 
sharp  image  of  an  object 
illuminated  by  ordinary 
white  light,  for  all  the  lines 
of  separation  between  light 

FIG.  445.  — Dispersion  produced  by  a  lens,     and    dark    portions    of    the 

image  will  be  colored. 

This  defect,  which  is  known  as  chromatic  aberration,  may  be 
remedied  by  combining  a  lens  of  crown  glass  with  a  lens  of 
flint  glass,  as  shown  in  figure  446. 
By  carefully  designing  the  two 
component  lenses  which  are  in 
contact,  it  is  possible  to  make 
achromatic  lenses,  which  produce  the 
necessary  refraction  without  dis- 
persion. The  two  parts  of  small 
achromatic  lenses  are  cemented  to- 
gether with  Canada  balsam. 

466.  Spectroscope.     In  the  spec- 
trum produced  by  a  prism  the  different  colors  overlap  each 
other  to  some  extent.     This  can  be  remedied  by  using  a, 


Converging      Diverging 
FIG.  446.  —  Achromatic  lenses. 


458 


PRACTICAL  PHYSICS 


spectroscope.  There  are  four  main  parts  in  a  spectroscope 
(Fig.  447):  the  collimator,  which  has  a  slit  at  one  end  and  a 
convex  lens  at  the  other  ;  a  prism,  commonly  of  flint  glass  ;  a 
telescope,  which  has  an  object  glass  and  eyepiece,  and  a  scale 
tube,  which  has  a  ruled  scale  at  one  end  and  a  lens  at  the  other. 
In  the  collimator  the  slit  is  at  the  principal  focus  of  the  lens, 
and  so  light  diverging  from  the  slit.is  made  parallel  by  the  lens 

before  it  reaches  the  prism. 
Here  it  is  refracted  and  dis- 
persed, each  color  going  off  as 
a  parallel  beam  in  its  own 


FIG.  447.  —  Spectroscope. 


direction.  The  telescope  forms  a  sharply  denned  image  of 
the  spectrum.  The  scale  tube,  which  is  added  to  locate  the 
parts  of  the  spectrum,  is  so  mounted  that  the  light  from  the 
illuminated  scale  is  reflected  from  the  second  face  of  the 
prism  into  the  telescope  along  with  the  spectrum. 

467.  Kinds  of  spectra.  The  spectrum  of  sunlight,  or  solar 
spectrum,  is  frequently  seen  in  summer  time  after  a  shower  in 
the  form  of  a  rainbow.  The  sunlight  is  refracted  and  dis- 
persed by  the  raindrops.  When  the  solar  spectrum  is  studied 
carefully  with  a  spectroscope,  it  is  found  not  to  be  a  contin- 
uous band  of  colors,  but  to  be  crossed  by  many  vertical  dark 
lines.  Since  these  lines  were  first  studied  by  a  German 
astronomer,  Fraunhofer,  they  are  known  as  Fraunhofer  lines. 

Not  all  sources  of  white  light  give  these  dark  lines.     For 


SPECTRA  AND   COLOR  459 

example,  an  electric  arc  lamp,  an  incandescent  lamp  with  a  car- 
bon filament,  an  ordinary  gas  flame  which  contains  many  par- 
ticles of  incandescent  solid  carbon  (soot),  and  indeed  all 
incandescent  solids  give  continuous  spectra. 

The  spectrum  of  an  incandescent  vapor  or  gas  is  quite 
different.  It  is  what  is  called  a  bright-line  spectrum,  and  is 
characteristic  of  the  substance  used. 

If  we  dip  a  platinum  wire  or  bit  of  asbestos  into  a  solution  of  common 
salt  (sodium  chloride)  and  hold  it  in  a  blue  Bunsen  flame,  we  get  a 
bright  yellow  flame.  If  we  examine  this  flame  with  a  spectroscope,  we 
see  a  bright  yellow  line  which  occupies  the  position  of  the  yellow  part  of 
the  spectrum.  This  yellow  light  comes  from  the  incandescent  sodium 
vapor. 

If  we  repeat  the  experiment  with  a  wire  dipped  in  a  chemical,  called 
lithium  chloride,  we  get  a  red  flame,  which  gives  in  the  spectroscope  two 
bands,  one  yellow  and  one  red.  Calcium  chloride  also  gives  two  bands, 
green  and  red.  (The  yellow  band,  which  is  likely  to  be  seen  also,  is  due 
to  sodium  present  as  an  impurity.) 

468.  Spectrum  analysis.     When  the  spectroscope  is  used 
to  examine  the  spectrum  of  other  gaseous  substances,  it  is 
found  that  each  element  has  its  own  characteristic  spectrum. 
It  may  be  simple  as  in  the  case  of  sodium,  or  it  may  be  com- 
plex as  in  the  case  of  iron  vapor,  which  has  more  than  four 
hundred  lines.     Since  a  very  small  quantity  of  a  substance 
will  show  its  characteristic  spectrum  lines  (for  example,  less 
than  one  millionth  of  a  milligram  of  sodium  can  be  detected), 
we  have  a  very  delicate   method   of   analyzing  substances. 
Spectrum  analysis  was  first  used  by  the  chemist  Bunsen  in  1859. 

469.  Absorption  spectra.     Kirchhoff  (1824-1887),  while  a 
professor  of  physics  at  Heidelberg,  worked  conjointly  with 
Bunsen  in  these  investigations  with  the  spectroscope.     Kirch- 
hoff observed  that  when  he  held  an  alcohol  flame  colored 
with  common  salt  in  front  of  the  slit  of  the  spectroscope  and 
allowed  a  beam  of   sunlight   to   pass  through  the  slit,  the 
sodium  line  became  especially  dark  and  sharp,  although  he  had 
expected  it  to  be  especially  bright.     He  concluded  that  the 


460 


PRACTICAL   PHYSICS 


sunlight  had  been  in  part  absorbed  by  the  yellow  sodium 
flame  and  that  the  special  part  had  been  removed  which  the 
sodium  flame  itself  ordinarily  gives  out.  This  fact  was 
generalized  by  Kirchhoff  in  the  following  law :  — 

A  glowing  gas  absorbs  from  the  rays  of  a  hot  light-source 
those  rays  which  it  itself  sends  forth. 

The  demonstration  of  Kirchhoff's  law  may  be  conveniently  performed 
with  the  apparatus  shown  in  figure  448.  The  source  of  light  L  is  the 
glowing  positive  carbon  of  the  electric  are,  whose  rays  are  made  parallel 
by  a  lens  O.  Two  strips  of  asbestos  board,  soaked  in  salt  water,  are 


FIG.  448. —  Absorption  of  light  by  sodium  vapor. 

heated  by  a  wing  top  Bunsen  burner.  The  light  from  the  electric  arc 
passes  directly  through  the  sodium  flame  into  a  "direct-vision"  spectro- 
scope which  disperses  the  light  on  the  screen  Sc. 

First  we  set  the  sodium  flame  burner  to  one  side,  and  produce  a  con- 
tinuous pure  spectrum  on  the  screen. 

Then  we  bring  the  sodium  flame  into  position,  and  we  see  in  the  yel 
low  portion  of  the  spectrum  a  dark  line. 

If  we  cover  the  lens  0  with  an  opaque  cardboard,  of  course  the  spec- 
trum disappears,  but  in  the  place  of  the  dark  line  we  now  have  the  bright 
sodium  line. 

Finally,  if  we  place  a  small  white  screen  with  a  narrow  slit  where  the 
dark  line  is  located  just  in  front  of  the  screen  Sc,  the  dark  line  on  the 
screen  Sc  shows  as  a  yellow  line. 

This  shows  that  the  dark  absorption  band  is  not  absolutely  black,  but 
is  so  much  less  intense  than  the  direct  radiation  from  the  arc  that  it  ap- 
pears black  by  contrast. 


SPECTRA  AND   COLOR  461 

It  is  evident,  then,  that  to  produce  Hack  absorption  lines 
the  absorbing  vapor  must  be  colder  than  the  luminous  source. 

470.  Meaning  of  Fraunhofer  lines.     We  have  said  in  sec- 
tion 467  that  the  solar  spectrum  contains  a  large  number 
of  dark  lines.     Kirchhoff  concluded  that  these  dark  lines 
were  caused  by  the  presence  in  the  glowing  solar  atmosphere 
of  those  substances  which  themselves  produce  bright  lines  in 
the  same  positions.     The  core  of  the  sun  is  at  a  very  high 
temperature  and  gives  forth  a  continuous  spectrum.     But 
this  core  is  surrounded  by  a  layer  of  gas  which  is  cooler  and 
absorbs  those  light  rays  which  it  itself  would  send  out.     On 
this  basis  he  concluded  that  such  metals  as  iron,  magnesium, 
copper,  zinc,  and  nickel  exist  as  vapors  in  the  solar  atmos- 
phere.    After   much   study  he  found  that  the  bright-line 
spectra  of  all  the  elements  on  the  earth  correspond  in  position 
to  certain  Fraunhofer  lines,  and  concluded  that  all  the  ele- 
ments found  on  the  earth  exist  in  the  atmosphere  of  the  sun. 
There  were  certain  other  Fraunhofer  lines  whose  elements 
were  not  known  on  the  earth  in  Kirchhoff's  time.     One  of 
these  new  elements,  helium,  has  since  been  found  on  the 
earth,  and  perhaps  the  others  also  will  sometime  be  found. 

Kirchhoff's  explanation  of  the  Fraunhofer  lines  was  epoch 
making.  Helmholtz  said,  "It  has  excited  the  admiration 
and  stimulated  the  fancy  of  men  as  hardly  any  other  dis- 
covery has  done,  because  it  has  permitted  an  insight  into 
worlds  that  seemed  forever  veiled  to  us." 

471.  The  nature  of  light.     We  have  said  that  light  is  con- 
sidered to  be  a  vibration  of  the  ether.     That  is,  light  and 
heat  are  both  forms  of  radiant  energy.     But  we  must  not 
think  that  this  has  always  been  the  accepted  theory.     To  be 
sure,  the  great  Dutch  physicist,  Huygens  (1629-1695),  worked 
out  very  completely  the  wave  theory,  but  his  rival,  Sir  Isaac 
Newton,  in  England,  maintained  the  older  corpuscular  theory, 
according  to  which  light  consists  of  streams  of  very  minute 
particles,  or  corpuscles,  projected   with  enormous  velocity 


462  PRACTICAL  PHYSICS 

from  all  luminous  bodies.  Newton's  reputation  as  a  scientist 
was  so  great  that  his  unfortunate  corpuscular  theory  con- 
trolled scientific  thought  for  more  than  a  hundred  years,  and 
it  was  not  until  the  beginning  of  the  nineteenth  century 
that  the  experiments  of  Thomas  Young  in  England  and  of 
Fresnel  in  France  placed  the  wave  theory  on  a  firm  basis. 

472.  Different  colors  due  to  different  wave  lengths.     It  is 
now  possible  to  measure  directly  the  length  of  the  waves  of 
light  of  different  colors,  and  to  show  that  the  waves  of  red 
light  are  longest  and  those  of  violet  are  shortest.     So  in  the 
dispersion  of  sunlight  by  a  prism,  it  is  the  long  waves  (red) 

I  which  are  refracted  least,  and  the  short  waves  (violet)  which 
are  refracted  most.  The  following  table  gives  the  approxi- 
mate wave  lengths  of  some  of  the  colors. 

WAVE  LENGTHS  OF  LIGHT 

Red,          0.000068  cm.  Green,     0.000052  cm. 

Orange,     0.000065  cm.  Blue,        0.000046  cm. 

Yellow,     0.000058  cm.  Violet,     0.000040  cm. 

473.  Colors  of  objects.     The  color  of  any  object  depends 
(1)  on  the  light  which  illuminates  it,  and  (2)  on  the  light  it 
reflects  or  transmits  to  the  eye. 

A  skein  of  red  yarn  held  in  the  red  end  of  the  spectrum  appears  red. 
But  when  held  in  the  blue  end  of  the  spectrum,  it  appears  nearly  black. 
Similarly  a  skein  of  blue  yarn  appears  nearly  black  in  all  parts  of  the 
spectrum  except  the  blue,  where  it  has  its  proper  color. 

Another  striking  experiment  is  to  illuminate  an  assortment  of  bril- 
liantly colored  worsteds  or  paper  flowers  by  the  light  from  a  sodium 
flame.  This  light  contains  but  one  group  of  wave  lengths.  Those  wor- 
steds which  reflect  these  wave  lengths  look  bright,  while  those  which  do 
not  reflect  them  look  dark.  They  all  look  either  yellow  or  dark. 

Thus  it  appears  that  when  a  piece  of  paper  looks  white  in 
daylight,  it  is  because  it  reflects  all  wave  lengths  equally, 
and  when  a  piece  of  cloth  looks  red  in  daylight,  it  is  because 
it  reflects  only  those  long  waves  which  produce  red  light. 
If  the  white  paper  receives  only  waves  of  red  light,  it  appears 


SPECTRA   AND   COLOR 


463 


red,  and  if  the  red  cloth  receives  only  waves  which  have  no 
red  in  them,  it  appears  dark.  That  is,  the  color  of  an  opaque 
object  depends  on  the  wave  length  of  the  light  it  reflects.  The 
Cooper-Hewitt  mercury  vapor  lamp  is  a  very  efficient  electric 
lamp,  but  it  cannot  be  used  in  places  when  colors  must  be 
distinguished,  for  it  does  not  furnish  waves  of  red  light. 

If  we  place  a  piece  of  red  glass  in  the  path  of  the  light  which  is  dispersed 
by  a  prism  to  form  a  spectrum,  we  see  only  the  red  portion  of  the  spectrum. 
This  shows  that  all  the  wave  lengths  except  the  long  red  ones  have  been 
absorbed.  In  a  similar  way  a  green  glass  lets  the  green  light  through,  but 
greatly  reduces  the  other  parts  of  the  spectrum.  If  we  insert  both  the 
green  and  the  red  glasses,  the  spectrum  almost  completely  vanishes. 

Thus  we  see  that  the  color  of  a  transparent  object  depends  on 
the  wave  length  of  the  light  it  transmits.  Ordinary  red  glass, 
such  as  photographers  use  for  their  red  lanterns,  transmits 
freely  only  red  light,  and  absorbs  almost 
completely  the  yellow,  green,  blue,  and 
violet  light,  which  especially  affect  the 
chemical  compounds  used  on  photo- 
graphic plates. 

474.  Mixing  colors  and  mixing  pig- 
ments. '  There  are  other  colors  besides 
white  which  do  not  have  a  definite  wave 
length.  A  mixture  of  several  wave 
lengths  may  produce  the  same  sensation 
as  a  single  wave  length. 

Let  us  rotate  a  disk  part  red  and  part  green 
(Fig.  449)  so  rapidly  that  the  effect  on  the  eye  is 
the  same  as  though  the  colors  came  to  the  eye 
simultaneously.  The  revolving  disk  appears  yel- 
low, much  like  the  yellow  of  the  spectrum.  By 
mixing  red  and  blue  we  get  purple,  which  is 
not  found  in  the  spectrum.  By  mixing  black 
with  red  or  orange  or  yellow  we  get  the  various  shades  of  brown. 

The  colors  of  the  spectrum  are  called  pure  colors  and  the 
others  compound  colors.     If  yellow  light  is  mixed  with  just 


FIG.  449.  —  Newton's 
color  disk. 


464 


PRACTICAL  PHYSICS 


the  right  tint  of  blue,  white  light  is  produced.     Such  colors 
are  called  complementary  colors. 

Let  us  pulverize  a  piece  of  yellow  crayon  and  a  piece  of  blue  crayon. 
If  we  mix  the  two  together  about  half  and  half,  the  color  of  the  resulting 
mixture  is  bright  green. 

This  shows  that  while  mixing  yellow  and  blue  light  pro- 
duces white,  mixing  yellow  and  blue  pigments  produces  green. 

This  is  because  the  yellow  pig- 
ment absorbs  or  subtracts  from 
white  light  all  except  yellow  and 
green,  and  the  blue  pigment  sub- 
tracts all  except  blue  and  green, 
therefore  the  only  color  not  ab- 
sorbed by  one  pigment  or  the 
other  is  green.  In  other  words,  in 
mixing  pigments,  the  color  of  the 
mixture  is  that  which  escapes  absorp- 
tion by  the  different  ingredients. 

475.  Colors  of  thin  films.  The 
brilliant  colors  produced  by  the  reflection  of  light  from  thin 
transparent  films,  like  the  film  of  a  soap  bubble,  furnishes 
one  of  the  strongest  arguments 
for  the  wave  theory  of  light. 

Let  us  bind  two  pieces  of  plate  glass 
A  and  B  (Fig.  450)  together  with  rub- 
ber bands,  in  such  a  way  that  they  will 
be  separated  at  one  end  by  a  piece  of 
tissue  paper  C.  If  we  hold  the  glass 
strips  behind  a  sodium  flame,  we  see  in 
the  reflected  image  of  the  yellow  flame 
a  series  of  horizontal  fine  dark  lines. 

To  explain  this  effect  we  will 
draw  a  much-enlarged  section  of 
the  glass  plates  with  the  wedge  _  2>2A 

?  £          FIG.  451.  —  Explanation  of  forma- 

Ol  air   between.       In   ngure   451  tion  of  bright  and  dark  lines. 


FIG.  450.  —  Interference  of  light 
waves. 


Interference 
Re-enforcement 
Interference 
'L  Re-enforcement 


SPECTRA  AND   COLOR  465 

let  AB  and  BC  be  the  glass  plates,  and  let  the  yellow  so- 
dium light  be  coming  from  the  right  as  a  series  of  trans- 
verse waves  which  we  can  represent  by  the  wavy  lines. 
We  know  that  this  light  is  in  part  transmitted  and  in  part 
reflected  at  each  glass  surface.  But  we  are  interested  only 
in  what  happens  at  the  interior  faces  AB  and  BO  of  the 
plates.  Let  the  full  line  DE  represent  the  light  reflected  at 
the  point  D  on  the  surface  AB,  and  let  the  dotted  line  D' E 
represent  the  wave  reflected  at  Dr  on  the  surface  BO.  If 
the  distance  from  D  to  D1  is  such  as  to  make  one  reflected 
wave  just  half  a  vibration  behind  the  other  in  phase,  they 
will  neutralize  each  other  or  interfere.  At  this  point  we  have 
a  dark  line.  But  at  another  point  F  the  distance  between 
the  plates  may  be  such  that  the  wave  reflected  at  F'  coin- 
cides with  or  reenforces  the  wave  reflected  at  F.  At  this 
point  we  see  a  bright  yellow  line.  If  we  select  any  two 
consecutive  dark  lines,  we  know  that  the  double  path  between 
the  plates  at  one  line  must  be  just  one  wave  length  longer 
than  that  at  the  other  line.  This  gives  us  a  method  of  com- 
puting the  length  of  a  wave. 

For  example,  we  may  compute  the  wave  length  of  sodium  light,  if  we 
know  the  length  of  the  air  gap,  the  thickness  of  the  paper  wedge,  and 
the  distance  between  two  dark  lines.  Thus  suppose  the  length  of  the 
air  wedge  is  100  millimeters,  the  thickness  of  the  paper  is  0.03  milli- 
meters, and  the  distance  between  adjacent  lines  is  1  millimeter.  Since 
the  width  of  the  wedge  increases  0.03  millimeters  in  a  distance  of  100 
millimeters,  it  increases  0.0003  millimeters  in  1  millimeter,  and  the  in- 
crease in  the  double  path  between  adjacent  dark  lines  would  be  0.0006 
millimeters.  This  is  approximately  the  wave  length  of  sodium  light. 

476.  Sunlight  decomposed  by  interference.  We  may  sub- 
stitute a  soap  film  for  the  wedge-shaped  air  film  used  in  the 
preceding  experiment,  and  illuminate  it  by  sunlight  instead 
of  the  yellow  light  of  the  sodium  flame. 

Let  us  dip  a  clean  wire  ring  into  a  soap  solution  and  set  it  up  so  that 
the  film  is  vertical.  The  water  in  the  film  will  run  down  to  the  lower 


466 


PRACTICAL  PHYSICS 


edge,  and  the  film  becomes  wedge-shaped.  Let  a  beam  of  sunlight,  01 
the  light  from  a  projection  lantern,  fall  on  this  soap  film  and  be  reflected 
to  a  white  screen.  Furthermore,  let  a  convex  lens  be  arranged,  as  in  fig- 
ure 452,  so  as  to  produce  a  sharp  image  of  the  film  F  on  the  screen  S. 

We  shall  see  on  the  screen  a  series 
of  horizontal  bands  of  the  various 
colors  of  the  spectrum. 

The  white  sunlight  is  com- 
posed of  different  colors  and 
so  of  different  wave  lengths. 
The  interference  of  the  red 
waves  takes  place  at  one 
point,  and  that  of  the  yellow 
at  a  different  point.  Where 
there  is  interference  of  the 
red  waves,  the  complemen- 
tary color,  a  sort  of  bluish- 
green  is  left ;  and  where 
there  is  interference  of  the 
yellow  waves,  the  color  com- 
plementary to  yellow,  namely,  blue,  is  produced.  In  this  way 
we  have  a  series  of  colored  bands  which  are  complementary 
to  all  the  colors  of  the  spectrum. 

Many  beautiful  color  effects  are  caused  by  the  interference 
of  light  waves  by  very  thin  films.  The  colors  of  oil  films  on 
the  surface  of  water,  of  the  thin  films  of  oxide  on  metals 
and  on  Venetian  glass,  of  the  feathers  of  the  peacock  and  of 
changeable  silk  are  due  to  the  interference  of  light  waves. 

477.  Infra-red  and  ultra-violet  rays.  In  the  last  few  years 
we  have  come  to  know  that  the  sun  is  sending  out  not  only 
the  light  waves  which  affect  the  optic  nerve,  but  also  other 
longer  ether  waves  which,  though  invisible,  yet  can  produce 
strong  heating  effects,  and  are  called  the  infra-red  rays  (Fig. 
453).  We  have  also  learned,  by  photographing  the  spectrum 
of  the  sun,  that  it  is  sending  out  rays  too  short  to  be  seen,  which 
affect  a  photographic  plate,  and  are  called  ultra-violet  rays. 


FIG.  452.  — Interference  of  white  light  in 
soap  film. 


SPECTRA   AND   COLOR  467 

478.  Electromagnetic  theory  of  light.  As  we  have  seen, 
Faraday  was  led  to  believe  that  his  "  lines  of  force  "  trans- 
mitted electricity  and  magnetism  through  some  medium, 
probably  the  ether.  A  few  years  later  Maxwell  developed 
this  theory  of  Faraday's  and  put  it  on  a  mathematical  basis. 
The  argument  was  finally  clinched  in  1887  by  a  young 
German,  Hertz.  His  experiments  proved  that  electric  waves 
really  exist,  and  have  the  same  velocity  as  light,  although 


Ultra- 
Violet 

A 

~400  700  1000  1500  2000 

FIG.  453.  — Chart  of  waves  of  varying  lengths. 

they  are  sometimes  many  meters  long.  These  electromag- 
netic waves  are  reflected  and  refracted  like  light  waves. 
Therefore,  we  feel  sure  that  light  waves  are  electric  waves.  This 
conception,  and  that  of  the  conservation  of  energy,  are  the 
most  remarkable  achievements  of  physics  in  the  nineteenth 
century. 

SUMMARY   OF  PRINCIPLES  IN  CHAPTER  XXIII 

Continuous  spectrum  formed  by  incandescent  solids. 
Bright-line  spectrum  formed  by  incandescent  gases. 
Dark-line  spectrum  formed  by  incandescent  solid  shining  through 
an  absorbing  layer  of  cooler  gas. 

Wave  length  of  visible  spectrum  ranges  from  about  0.000068  cm. 
(red)  to  about  0.000040  cm.  (violet). 

Short  waves  most  refracted  by  prism. 

Color  of  an  object  depends  on  wave  lengths  reaching  eye. 
Colors  of  thin  films  due  to  disappearance  of  certain  wave  lengths 
by  interference. 


468  PRACTICAL  PHYSICS 

QUESTIONS 

1.  A  clean  platinum  wire  is  held  in  a  blue  Buiisen  flame  and  observed 
through  a  spectroscope.     What  sort  of  a  spectrum  would  you  expect  to 
get? 

2.  What  kind  of  Fraunhofer  lines  must  one  get  in  the  light  of  the 
moon? 

3.  What  kind  of  a  spectrum  would  you  get  if  you  looked  at  the 
mantle  of  a  Welsbach  lamp  through  a  spectroscope  ? 

4.  The  cpmplete  spectrum  of  the  sun's  rays  is  said  to  consist  of  three 
parts :  heat  spectrum,  light  spectrum,  and  chemical  spectrum.     Explain 
the  appropriateness  of  these  terms. 

5.  What  causes  the  various  colored  lights  used  in  fireworks? 

6.  Why  does  a  blue  dress  look  black  by  the  light  of  a  kerosene  lamp  ? 

7.  Why  does  a  reddish  lampshade  make  a  room  seem  more  cheerful 
at  night? 

8.  How  are  colored  moving  pictures  produced? 

9.  Why  do  they  not  use  glass  lenses  in  the  ultra-violet  microscope? 
10.   What  sort  of  waves  are  used  in  wireless  telegraphy? 


CHAPTER   XXIV 


ELECTRIC  WAVES :   ROENTGEN   RAYS 

Discharge  of  condenser  is  oscillatory  —  electrical  resonance 
—  electric  waves  —  detectors —  wireless  telegraphy. 

Discharge  through  gases  —  cathode  rays  —  Roentgen  rays  — 
radium. 

ELECTRICAL  WAVES 

479.  Discharge  of  Leyden  jar  is  oscillatory.  In  1842 
Joseph  Henry  discovered  that  when  a  Leyden  jar  was  dis- 
charged through  a  coil  of  wire  surrounding  a  steel  needle, 
the  needle  was  magnetized.  Not  only  that,  but  he  was 
astonished  to  find  that  sometimes  one  end  was  made  the 
north  pole  and  sometimes  the  other,  even  though  the  jar  was 
always  charged  the  same  way. 
He  accounted  for  this  fact  by 
supposing  that  the  discharge  cur- 
rent kept  reversing  back  and 
forth,  that  these  oscillations  grad- 
ually died  away,  and  that  the 
direction  in  which  the  needle  was 
magnetized  depended  on  which 
way  the  last  perceptible  oscilla- 
tion happened  to  go.  This  oscillatory  current  is  represented 
by  the  curve  in  figure  454. 

A  few  years  later  Lord  Kelvin,  the  great  English  physicist 
and  engineer,  proved  mathematically  that  the  discharge  must 
be  oscillatory.  Finally,  in  1859,  Fedclersen  succeeded  in 
photographing  an  electric  spark  by  means  of  a  rapidly  rotat- 

469 


FIG.  454.  —  Oscillatory  electric 
discharge. 


470 


PRACTICAL  PHYSICS 


ing  mirror.  Figure  455  shows  such  a  photograph.  The 
oscillatory  discharge  is  drawn  out  into  a  band  by  the  rotating 
mirror,  and  thus  makes  a  zigzag  trace  on  the  camera  plate. 
From  this  experiment  it  is  possible  to  calculate  the  time  of 
one  oscillation.  It  is  exceedingly  short,  varying  from  one 
one-thousandth  to  one  ten-millionth  of  a  second. 

480.  Electrical  resonance.  The  frequency  of  the  oscillatory 
current  produced  by  discharging  a  condenser  depends  upon 
the  capacity  of  the  condenser,  and  upon  the  resistance  and 
self-induction  of  the  circuit  through  which  the  current  surges. 
Now  we  have  already  seen,  in  studying 
sound  waves,  that  two  objects  having  the 
same  frequency  of  vibration  tend  to  vibrate 
in  sympathy,  and  that  this  property  of  a 
vibrating  body  is  called  resonance.  Mechan- 
ical resonance  also  occurs  in  the  case  of 
two  pendulums. 

Let  us  stretch  a  piece  of  rubber  tubing  between 
two  supports  and  suspend  two  weights  x  and  y  by 
threads  of  equal  length,  as  shown  in  figure  456.  If 
we  set  one  pendulum  y  swinging,  the  other  pen- 
dulum x  soon  begins  to  swing,  and  the  first  one 
dies  down  as  energy  flows  across  to  the  other.  This 
will  happen  only  if  the  pendulums  are  of  the  same  length  and  so  of  the 
same  frequency.  That  is,  resonance  is  necessary  for  the  transfer  of  energy. 


FIG.  456.  —  Resonance 
in  two  pendulums. 


In  a  similar  way,  if  two  Leyden  jar  circuits  have  the  same 
capacity  and  the  same  self-induction,  they  will  have  the  same 
frequency,  and  one  circuit  will  influence  the  other. 

In  figure  457  let  A  and  £  be  two  Leyden  jars  of  the  same 
size  and  thickness  of  wall.  To  the  jar  A  is  connected  a  rec- 
tangular circuit  of  thick  wire,  one  end  of  which  touches  the 
outer  coating  of  the  jar,  while  the  other  is  separated  from 
the  knob  of  the  jar  by  a  small  spark  gap.  The  jar  B  is  con- 
nected to  a  similar  circuit,  except  that  the  end  CD  of  the 
rectangle  can  be  slid  back  and  forth,  and  there  is  no  spark 


FIG.  455  (in  upper  comer).  —Oscillations  of  electric  spark. 

FIG.  466. —X-ray  picture  of  a  broken  ankle,  which  had  been  called  "sprained" 
by  a  doctor.    Taken  in  a  physics  laboratory  by  the  brother  of  the  patient. 


ELECTRIC   WAVES:   ROENTGEN  RAYS 


471 


gap.  Finally,  let  the  inner  coating  of  B  be  connected  to  its 
outer  coating  by  a  strip  of  foil  cut  sharply  across  at  X. 

If  we  place  the  two  electrical  cir- 
cuits a  foot  apart  and  parallel,  and 
send  sparks  across  the  gap  of  A  by 
means  of  an  induction  coil,  we  find 
that  there  is  a  position  of  the  slider 
CD  such  that  tiny  sparks  appear  at 
the  gap  X  in  the  foil  strip  on  B. 
When  the  slider  is  moved  a  short  dis- 
tance from  this  position  either  way, 
the  sparks  at  X  cease. 

This   phenomenon  is  called 

electrical    resonance.        Although     FIG.  457. -Resonance  between  elec- 
, .        ,  trical  circuits. 

there  is  no  connection  between 

the  two  circuits,  yet  the  energy  in  one  circuit  surges  over 
into  the  other,  which  is  in  tune  with  it,  and  causes  a  spark 
there.  In  seeking  for  an  explanation  of  this  experiment, 
and  many  others,  we  must  conclude  that  an  oscillatory  dis- 
charge or  spark  sends  out  waves  in  the  surrounding  ether. 
The  ether  does  for  the  electric  circuits  what  the  rubber 
tubing  did  for  the  pendulums.  It  serves  as  a  medium  for 
the  transfer  of  energy. 

These  electric  waves  were  first  detected  and  measured  by 
Hertz,  in  1888,  and  are  therefore  called  Hertzian  waves.  They 
travel  with  the  same  velocity  as  light. 

481.  Electric  wave  detectors.  Very  sensitive  means  for  de- 
tecting these  electric  waves  have  been  invented.  One  means, 
invented  by  Branly  and  used  by  Marconi  in  his  first  wireless 
telegraphs,  is  called  a  coherer.  It  consists  of  a  small  glass 
tube  closed  at  each  end  by  metal  pistons.  A  space  of  a  mil- 
limeter or  two  between  the  pistons  is  filled  with  rather  coarse 
filings  of  nickel  and  silver.  When  electric  waves  fall  on 
this  coherer,  the  mast:  of  filings  "  coheres  "  or  sticks  together 
and  becomes  a  conductor.  A  slight  tap  causes  the  resistance 
of  the  coherer  to  return  to  its  original  high  value. 


472 


PRACTICAL  PHYSICS 


The  microphone,  described  in  section  310,  is  an  excellent 
wave  detector.  Another  form,  called  a  crystal  detector,  con- 
sists of  a  piece  of  silicon,  or  of  any  one  of  several  crystal- 
line substances,  such  as  galena,  embedded  in  soft  metal 
on  one  side  and  touched  on  the  other  by  a  metal  point.  In 
the  electrolytic  detector  a  fine  metal  point  just  touches  the  sur- 
face of  a  conducting  solution  or  electrolyte.  The  operation 
of  crystal  and  electrolytic  detectors  seems  to  depend  on  some 
mysterious  property  whereby  they  let  electricity  flow  through 
them  in  one  direction  much  more  easily  than  in  the  other. 

482.    Wireless   telegraphy.      Through   the   efforts   of   the 
Italian  inventor,  Marconi,  and  many  others,  electric  waves 
are  now  being  extensively  used  in  wireless 
telegraphy. 

A   simple  sending  station,  such  as  Marconi 
used  in  his  earliest  experiments,  is  shown  in 
figure  458.     The  essential  part  is  a  conductor 
called  the  aerial  or  antenna,  extending  to  a  con- 
siderable height  above  the  ground.     Powerful 
electrical  oscillations  are  set  up  in  this  con- 
ductor, like  the  oscillations  in  the  spark  dis- 
charge  shown   in   figure   455.      These    send 
waves  out  through  the  ether, 
just  as  a  stick  laid  on  water 
and    shaken    up    and    down 
sends   out   ripples    over    the 
surface  of  the  water. 

One  way  to  set  up  oscilla- 
tions in  an  aerial  is  to  put  a 
spark  gap  in  it,  and  to  send 
sparks  across  this  gap  by 


H: 

BATTERV 

FIG.  458.  —  Simple  sending  station. 


means  of  an  induction  coil  fed  by  batteries,  as  in  figure  458. 
Another  way  is  to  put  a  condenser  in  parallel  with  the  gap  in 
the  aerial,  and  to  fill  the  condenser  many  times  a  second  by 
means  of  a  step-up  transformer  fed  by  an  alternating  current. 


ELECTRIC   WAVES:  ROENTGEN  RAYS 


473 


Such  a  condenser  will  send  a  spark  across  the  gap  each  time 
it  fills.  Another  way  is  to  put  a  very  high  frequency  alter- 
nating current  dynamo  in  the  place  of  the  spark  gap  in  the 
antenna. 

The  simplest  kind  of  a  receiving  station  is  represented  in 
figure  459.  There  is  an  aerial  like  that  at  the  sending  sta- 
tion, except  that  instead  of  a  spark  gap,  it  contains  a  detector 
of  some  sort.  In  parallel  with  this  detector  is  a  telephone 
receiver.  Every  time  a  train  of  waves 
reaches  such  a  receiving  station,  some 
of  the  energy  is  absorbed  by  the  aerial, 
and  electrical  oscillations  are  set  up  in 
it.  These  cannot  get  through  the  tele- 
phone because  of  its  self-induction,  and 
so  they  have  to  pass  through  the  de- 
tector. But  since  a  crystal  detector 
lets  more  electricity  through  one  way 
than  the  other,  an  excess  of  electricity 
accumulates  in  the  antenna.  This  ex- 
cess then  discharges  through  the  tele- 
phone, and  the  diaphragm  moves  over 
and  back  once.  Since  this  happens 
every  time  a  train  of  waves  comes  in, 
which  is  many  times  every  second,  as 
long  as  the  key  of  the  sending  station 
is  closed,  the  telephone  diaphragm  is  FIG.  459.  —  A  simple  receiv- 
kept  vibrating  and  emits  a  steady  mg  station, 

musical  note.  The  duration  of  this  note  can  be  made  shorter 
or  longer  by  holding  the  sending  key  down  a  shorter  or  a 
longer  time,  and  so  the  dots  and  dashes  of  the  Morse  code 
can  be  transmitted. 

The  circuits  used  in  commercial  wireless  telegraphy  are 
much  more  complicated  than  these,  because  it  is  necessary 
to  "  tune  "  the  sending  and  receiving  stations  accurately  to 
the  same  frequency,  and  to  make  them  insensitive  to  waves 


474  PRACTICAL  PHYSICS 

of  any  other  frequency,  so  that  one  pair  of  stations  may  not 
interfere  with  another.  For  an  explanation  of  commercial 
sending  and  receiving  stations  the  reader  may  consult  any 
of  the  numerous  popular  or  technical  books  on  wireless 
telegraphy. 

Wireless  telegraphy  is  now  used  on  all  ocean  steamships, 
so  that  they  are  in  constant  communication  with  other  ships 
or  with  land  stations.  Timely  aid  has  thus  been  called  to 
ships  in  distress.  Warships  are  kept  in  touch  with  the  naval 
headquarters  of  their  governments,  which  have  powerful 
sending  stations.  One  of  the  largest  of  these  uses  the  Eiffel 
Tower  in  Paris  as  the  support  of  its  antenna,  and  sends  out 
time  signals  to  ships  all  over  the  Atlantic  Ocean.  Messages 
have  been  sent  even  as  far  as  across  the  Atlantic  Ocean  by 
the  Marconi  stations  at  Wellfleet,  Cape  Cod,  Massachusetts, 
and  at  Poldhu,  England. 

483.  Wireless  telephony.  A  wireless  sending  station  ordi- 
narily sends  out  wave  trains  at  unvarying  intervals,  1000 
every  second,  because  it  is  fed  by  an  alternating  current  of 
unvarying  frequency,  say  500  cycles  per  second,  and  emits  one 
wave  train  for  every  loop  of  the  current.  Since  the  tele- 
phone diaphragm  of  the  receiving  station  moves  once  for 
each  train  received,  its  vibration  is  also  at  a  uniform  rate 
(1000  vibrations  per  second  in  the  case  just  mentioned)  and 
it  emits  a  musical  note  of  unvarying  pitch.  Recently  send- 
ing stations  have  been  devised  that  emit  wave  trains  at  vary- 
ing intervals  corresponding  to  the  varying  pitches  and  qual- 
ities of  human  speech.  When  such  a  succession  of  wave 
trains  falls  on  an  ordinary  wireless  receiving  station  the  dia- 
phragm in  its  telephone  vibrates  like  the  diaphragm  of  an 
ordinary  telephone  receiver,  or  like  the  diaphragm  of  a  phon- 
ograph, and  emits  speech.  Wireless  telephone  messages  can  be 
picked  up  by  any  one  who  has  a  properly  tuned  wireless  tele- 
graph set.  Wireless  telephony  is  alread}7  practicable  over  con- 
siderable distances,  but  is  not  yet  (1913)  a  commercial  success. 


ELECTRIC    WAVES:   ROENTGEN  BATS  475 


ELECTRICAL  DISCHARGE  THROUGH  GASES 

484.  Sparking  voltage.     The  voltage  needed  to  make  a 
spark  jump  between  two  knobs  depends  on  several  factors, 
such  as  the  size  of  the  knobs,  the  distance  between  them,  and 
the  atmospheric  pressure.     It  takes  less  voltage  to  cause  a 
spark  to  jump  between  two  sharp  points  than  between  two 
round  balls.     For  example,  the  sparking  voltage  for  two  sharp 
points  1  centimeter  apart  is  about  7500  volts,  and  for  two 
round  balls  1  centimeter  in  diameter  and  1  centimeter  apart 
is  about  27,000  volts.     The  sparking  voltage  between  two 
sharp  points  varies  so  nearly  as  the  distance  that  this  is  a 
method  used  to  measure  very  high  voltage. 

To  show  the  effect  of  atmos- 
pheric pressure  we  may  connect 
a  glass  tube  2  or  3  feet  long  with 
an  induction  coil,  as  shown  in 
figure  460.  The  tube  is  connected 
with  a  vacuum  pump  by  a  side 
tube.  When  the  coil  is  first 
started,  the  discharge  takes  place 
between  x  and  y,  the  terminals  of 
the  coil,  which  are  only  a  few  FIG.  460.  —  Discharge  in  partial  vacuum, 
millimeters  apart,  but  as  the  air 

is  pumped  out  of  the  tube,  the  discharge  goes  through  the  long  tube  in- 
stead* of  across  the  short  gap  xy.  This  shows  that  the  sparking  voltage 
decreases  when  the  pressure  is  diminished. 

485.  Discharges  in  partial  vacua.     Reducing  the  atmos- 
pheric pressure  between  two  points  makes  it  easier  for  an 
electric  discharge  to  pass,  until  a  certain  point  in  the  exhaus- 
tion is  reached.     Then  it  begins  to  be  more  difficult.     At 
the  very  highest  degree  of  exhaustion  yet  attainable  it  is 
hardly  possible  to  make  a  spark  pass  through  a  vacuum  tube. 

The  changes  in  the  appearance  of  such  a  tube  as  the  ex- 
haustion proceeds  are  very  interesting.  At  first  the  dis- 
charge is  along  narrow  flickering  lines,  but  as  the  pressure 


476 


PRACTICAL  PHYSICS 


Fia.  461.  — Geissler  tube,  made  to  study 
spectra  of  hydrogen. 


is  lowered,  the  lines  of  the  discharge  widen  out  and  fill  the 
whole  tube  until  it  glows  with  a  steady  light.  With  still 
higher  exhaustion,  a  soft,  velvety  glow  covers  the  surface  of 
the  negative  electrode  or  cathode,  while  most  of  the  tube  is 
filled  with  the  so-called  positive  column  which  is  luminous 
and  stratified,  and  reaches  to  the  anode.  The  so-called 

Geissler  tubes  (Fig.  461) 
are  little  tubes  of  this  sort 
which  are  usually  made  in 
fantastic  shapes  and  serve 
as  pretty  toys.  The  color  of  the  light  from  a  Geissler  tube 
depends  on  the  gas  which  is  in  the  tube,  and  on  the  kind 
of  glass  used. 

486.  Cathode  rays.  When  the  exhaustion  of  a  tube  is 
carried  to  a  very  high  degree,  so  that  the  pressure  is  equal 
to  about  0.0001  of  a  millimeter  of  mercury,  the  positive  glow 
is  very  faint  and  the  dark  space  around  the  cathode  is  per- 
vaded by  a  discharge.  An  invisible  radiation  streams  out 
nearly  at  right  angles  to  the  cathode  surface,  no  matter  where 
the  anode  is  located  in  the  tube.  This  radiation  from  the 
cathode  is  called  cathode  rays  and  shows  itself  in  several 
ways  :  first  by  a  yellowish  green  fluorescence 
wherever  it  strikes  the  glass  of  the  tube ; 
second,  by  the  fact  that  it  can  be  brought  to 
a  focus  where  it  produces  intense  heat ;  and 
third,  by  the  sharply  defined  shadows  which 
a  metal  interposed  in  its  path  produces  in 
the  fluorescence  on  the  end  of  the  tube. 

A  Crookes'  tube,  arranged  as  in  figure  462,  shows 
the  heating  effect  of  the  cathode  rays.  When  an  in- 
duction coil  sends  a  discharge  through  the  tube  from 
top  to  bottom,  the  cathode  rays  are  focused  on  a  piece 
of  platinum  which  becomes  red  hot. 

Another  Crookes' tube,  arranged  as  in  figure  463,  FlG  452.  —  Heating 
shows  that  a  shadow  is  formed  on  the  end  of  the  tube  effect  of  cathode 
by  an  aluminum  cross.  rays. 


ELECTRIC   WAVES;  ROENTGEN  BATS 


477 


FIG.  463.  —  Shadow  formed  by 
cathode  rays. 


487.   Bending    of    cathode    rays. 

A  Crookes'  tube,  made  as  in  figure 

464,     sends    a     narrow    band    of 

cathode  rays  through  the  slit   8  in 

the  aluminum    screen   mn  against 

a  fluorescent  screen  /  slightly  in- 
clined to  them.     When  a  strong 

magnet  M  is  held  near  the  side  of 

this   tube,   it    is    found   that    the 

stream  of  cathode  rays  is  deflected 

in  the  direction  which  would  be  expected  if  they  were  a  stream 

of  negatively  charged  particles.  From  this  and  other  experi- 
ments we  believe  that  cathode  rays  are  nega- 
tively  charged  particles  projected  at  very  high 
velocity  from  the  cathode. 

J.  J.  Thomson,  the  English  physicist,  has 
estimated  from  various  experiments  on  cath- 
ode rays  that  the  negatively  charged  particles, 
which  he  calls  electrons,  have  each  a  mass 
about  sixteen  hundred  times  smaller  than 
that  of  a  hydrogen  atom,  and  move  with  a 
velocity  of  from  one  tenth  to  one  third  that 
of  light.  It  is  supposed  that  each  particle 
carries  a  negative  charge  of  electricity  equal 
to  that  of  the  hydrogen  atom  in  electrolysis. 

FIG.  464.— Bending      488.    Roentgen   rays.     In  1895,  while  ex- 
of  cathode  rays  by  perimenting   with  a  vac- 

a  magnet.  ° 

uum  tube,  Koentgen  dis- 
covered another  kind  of  rays  which  he 
called  X-rays.  When  cathode  rays  strike 
against  a  platinum  target,  as  shown  in 
figure  465,  Roentgen  rays  are  sent  off 
from  this  target.  They  affect  a  photo- 
graphic plate  somewhat  as  sunlight  does  ; 
but,  like  cathode  rays,  they  will  penetrate 


Lai 


X-ray  Field 


FIG.  465. —Roentgen  ray 
tube. 


478  PRACTICAL  PHYSICS 

many  substances  opaque  to  ordinary  light,  such  as  wood, 
pasteboard,  and  the  human  body.  That  they  are  not  the 
same  as  cathode  rays  is  shown  by  the  fact  that  they  are  not 
deflected  by  a  magnet. 

When  a  photographic  plate,  inclosed  in  the  usual  plate- 
holder  with  sides  of  hard  rubber  or  pasteboard,  is  exposed, 
with  a  hand  held  over  it,  to  Roentgen  rays,  a  shadow  pic- 
ture like  that  seen  on  the  fluorescent  screen  is  formed. 

We  may  demonstrate  the  action  of  Roentgen  rays  by  operating  an 
X-tube  with  an  induction  coil,  and  holding  a  fluorescent  screen  in  front 
of  the  bulb.  If  the  room  is  dark  and  the  hand  is  interposed  between 
the  tube  and  the  screen,  the  flesh,  which  is  easily  penetrated  by  the  rays, 
will  be  seen  faintly  outlined,  while  the  bones  will  cast  a  strong  shadow. 

Figure  466  (opposite  page  478)  is  from  a  photograph  taken  by  means 
of  X-rays,  and  shows  how  valuable  they  are  to  doctors. 

Roentgen  rays  are  produced  at,  and  sent  forth  from,  any 
solid  body  upon  which  cathode  rays  fall.  They  are  now 
known  to  be  ether  waves,  just  like  light  waves  and  wireless 
telegraph  waves,  but  of  very  short  wave  length. 

489.  Radioactivity.  Near  the  end  of  the  nineteenth  cen- 
tury, scientists  discovered  that  something  which  resembles 
Roentgen  rays  is  radiated  from  certain  rare  minerals,  such 
as  uranium,  pitch-blende,  and  thorium.  It  affects  a  photo- 
graphic plate  through  an  envelope  of  black  paper.  It  has 
also  the  power  of  discharging  electrified  bodies,  and  so  by 
using  a  very  sensitive  electroscope  it  is  possible  to  detect 
and  measure  the  intensity  of  this  radiation.  This  new  phe- 
nomenon is  called  radioactivity,  and  a  new  element,  which 
is  remarkably  radioactive,  has  been  discovered  and  called 
radium.  ,  In  this  interesting  and  novel  field  of  research  many 
scientists  are  now  seeking  to  learn  the  answer  to  the  great 
questions  "  What  is  electricity  ?  "  and  "  What  is  inside  the 
atoms  of  substances?" 


INDEX 


(Numbers  refer  to  pages.) 


Aberration,  lens,  442 ;    mirror,  418. 

Absolute,  pressure,  92 ;  temperature, 
182;  zero,  183. 

Absorption  of  gases,  100. 

Absorption  spectra,  459. 

A.  C.,  see  Alternating  current. 

Acceleration,  135,  149;  of  gravity,  142. 

Achromatic  lens,  457. 

Adhesion,  73. 

Aeroplane,  115. 

Air,  compressibility  of,  78,  80 ;  ex- 
pansion of,  180 ;  weight  of,  84. 

Air-brake,  79 ;  -compressor,  78 ;  -lift 
pump,  98. 

Alternating  current,  322.  358  to  373; 
power,  370. 

Alternator,  322,  363. 

Altitude  by  barometer,  91. 

Amalgamation,  265. 

Ammeter,  284. 

Ampere,  283,  287. 

Amplitude,  379,  387. 

Aneroid  barometer,  89. 

Anode,  283. 

Arc,  334;  automatic  feed,  335;  in- 
closed, 336  ;  naming,  336  ;  mercury, 
336. 

Archimedes'  principle,  59. 

Armature,  of  bell,  275;  of  circuit- 
breaker,  333;  drum,  326,  342;  of 
generator,  321,  362 ;  Gramme  ring, 
323,  370;  of  motor,  340;  station- 
ary, 364. 

Astigmatism,  447. 

Atmosphere,  moisture  in,  211 ;  pres- 
sure of,  85,  88 ;  refraction  in,  430. 

Attraction,  electric,  248 ;  magnetic, 
238 ;  molecular,  73. 

Audibility,  limits  of,  388. 


Back  e.  m.  f.,  343. 

Balance,  platform,  8 ;  spring,  8. 

Ball  bearings,  43. 

Balloon,  95. 

Banking  rails,  149. 

Barograph,  90. 

Barometer,  88. 

Battery,  263;  best  arrangement  of, 
295;  Edison  storage,  354;  lead 
storage,  352. 

Beam,  stiffness  and  strength  of,  128. 

Beats,  394. 

Bell,  Alexander  Graham,  313. 

Bell,  electric,  275. 

Belting,  38. 

Bending,  121,  123. 

Bicycle  pump,  78. 

Binocular,  452. 

Boiler,  221. 

Boiling  point,  172,  205  ;  effect  of  pres- 
sure on,  205  ;  table  of,  207. 

Bound  charge,  256. 

Bourdon  gauge,  68,  92. 

Boyle's  law,  80. 

Breaking  strength,  124. 

Bridge,  pinned,  114;  riveted,  114; 
girder,  115;  Wheatstone,  302. 

British  thermal  unit  (B.  t.  u.),  196. 

Bugle,  400. 

Bunsen,  459  ;  photometer,  409. 

Buoyancy,  in  air,  94 ;  in  liquids,  58. 

Calorie,  196. 
Camera,  443. 
Candle  power,  338,  409. 
Capacity,  256. 
Capillarity,  74. 

Carbon,  filament,  337 ;  microphone, 
314,  472  ;  transmitter,  314. 


479 


480 


INDEX 


Carbureter,  230. 

Cathode,  283  ;  rays,  476. 

Cell,  chemistry  of,  265  ;  Daniell,  269  ; 
dry,  270;  gravity,  269;  ions  in, 
266;  local  action  in,  268;  sal- 
ammoniac,  270 ;  storage,  352 ;  vol- 
taic, 263. 

Center,  of  gravity,  20;  of  curvature, 
417. 

Centigrade  scale,  172. 

Central  battery  system,  315. 

Centrifugal  pump,  97. 

Centripetal  force,  148. 

Chemical  effects  of  currents,  348. 

Circuit,  electric,  264. 

Circuit  breaker,  333. 

Clarinet,  400. 

Clinical  thermometer,  173. 

Clouds,  214. 

Coefficient,  of  expansion,  176,  178,  181 ; 
of  friction,  41,  117. 

Coherer,  471. 

Cohesion,  73,  148. 

Cold  storage,  216. 

Color,  462  to  466. 

Columbus,  239. 

Commercial  rating  of  electric  lights, 
337. 

Commutator,  322,  325  ;  -motor,  368. 

Compass,  239. 

Complementary  colors,  464. 

Component,  111. 

Composition  of  forces,  108. 

Compound,  color,  463  ;  engine,  225. 

Compound-wound  generator,  328. 

Compressed  air,  79. 

Compressibility  of  fluids,  78. 

Compression,  121,  123. 

Compression  members,  114: 

Compressors,  air,  78. 

Condenser,  electric,  256;  steam,  220, 
226. 

Conductance,  294. 

Conduction,  of  electricity,  249 ;  of 
heat,  189. 

Conjugate  foci,  for  lens,  439 ;  for 
mirror,  421. 

Conservation  of  energy,  164. 

Controller,  346. 

Convection,  186. 

Cooper-Hewitt  lamp,  336 ;  color  of,  463. 


Corliss  valve,  224. 

Cornet,  400. 

Coulomb,  283. 

Coulombmeter,  284. 

Crane,  23,  35,  108,  118. 

Critical  angle,  435. 

Crookes'  tube,  476. 

Crystal  detector,  472. 

Current,  alternating,  322  ;   convection, 

186 ;   direct,  322  ;  electric,  264,  283  ; 

heating  effect  of,  333  ;  induced,  309  ; 

magnetic   field   about,   272 ;    water, 

283. 

Curtis  turbine,  228. 
Curvature,  center  of,  417. 
Cycles,  365 

Damping,  362. 

Daniell  cell,  269. 

Davy,  334. 

Declination,  239. 

Density,  9  ;  table  of,  9  ;  of  air,  83  ;  of 
water,  179. 

Derrick,  23,  35. 

Detectors,  471. 

Dew,  213. 

Dew  point,  212. 

Dielectric,  257. 

Diffusion,  of  gases,  101 ;   of  light,  414. 

Dip,  239. 

Direct  current  (D.  C.),  322  ;  generator, 
323  ;  motor,  342  ;  power,  329  ;  uses 
of,  274  to  279,  332  to  355. 

Discord,  395. 

Dispersion,  457. 

Distillation,  207. 

Double-acting  pump,  97. 

Drum,  400. 

Drum  armature,  323,  326,  342,  362. 

Dry  cell,  270. 

Dry  dock,  61. 

Dynamo,  318,  321  to  329 ;  alternating 
current,  363  to  367;  energy  source 
in,  329  ;  kinds  of,  326,  328  ;  rule,  319. 

Dyne,  151. 

Earth,  as  magnet,  241. 
Echo,  385. 
Eddy  currents,  361. 
Edison,  incandescent  lamp,  337  *,  phon- 
ograph, 401 ;  storage  battery,  354. 


INDEX 


481 


Efficiency,  defined,  43  ;  of  air-lift  pump, 
98;  of  boiler,  223;  of  Edison  cell, 
355 ;  of  electric  lights,  338 ;  of  gas 
engine,  233;  of  motor,  346;  of 
steam  engine  compared  with  gas 
engine,  234 ;  of  steam  plant,  226 ; 
of  steam  turbine,  230 ;  of  storage 
cell,  354;  of  transformer,  359;  of 
water  turbine,  72. 

Elastic  limit,  124. 

Electric,  arc,  334;  attraction,  248; 
bell,  275  ;  circuit,  264  ;  current,  263  ; 
generator,  318,  321  to  329,  363  to 
367;  heating,  332;  lighting,  334; 
machines,  frictional,  252  ;  machines, 
induction,  259  ;  motor,  340  ;  power, 
329;  waves,  471;  welding,  360; 
whirl,  253  ;  work,  330. 

Electricity,  two  kinds  of,  250. 

Electro,  -chemical  equivalent,  351 ; 
-magnet,  274 ;  -magnetic  theory  of 
light,  467;  -plating,  349;  -statics, 
248;  -typing,  350. 

Electrolysis,  348. 

Electrolytic,  copper,  351 ;  detector, 
472. 

Electromotive  force,  267;  back,  343; 
of  cell,  288 ;  induced,  309,  319  ;  unit 
of,  286. 

Electrons,  260. 

Electrophorus,  259. 

Electroscope,  250 ;  condensing,  264. 

Energy,  157  ;  chemical,  163  ;  conserva- 
tion of,  164 ;  equation,  159  ;  kinetic, 
157 ;  potential,  162 ;  transforma- 
tions of,  163. 

Engine,  balance  sheet  of,  234;  com- 
pound, 225;  condensing,  226;  Cor- 
liss, 224  ;  4-cycle,  232  ;  hot  air,  185  ; 
internal  combustion,  230;  recipro- 
cating, 227  ;  slide  valve,  223  ;  single 
acting,  231;  steam,  219;  2-cycle, 
231. 

Equilibrant,  107. 

Equilibrium,  conditions  of,  26. 

Erg,  161. 

Ether,  192,  243,  471,  478. 

Evaporation,  210. 

Exciter,  364. 

Expansion,  coefficient  of,  176,  178,  181 ; 
in  freezing,  200 ;  of  gases,  180 ;  of 

2l 


liquids,     178;      of    solids,   174;     of 
steam,  225 ;    of  water,  179. 
Eye,  445 ;  defects  of,  446. 

Factor  of  safety,  125. 

Fahrenheit  scale,  172. 

Falling  bodies,  140 ;  acceleration  of, 
142 ;  laws  of,  143. 

Faraday,  electromagnet,  275,  308,  318 ; 
field  around  magnet,  242  ;  properties 
of  lines  of  force,  243 ;  transformer, 
358. 

Faucet,  67. 

Feddersen,  on  spark  discharge,  469. 

Field,  of  generator,  321,  327,  364; 
magnetic,  242  ;  of  motor,  340,^§8 ; 
revolving,  364  ;  rotating,  368  ;  side 
push  of,  340. 

Field  glass,  452. 

Filament,  incandescent,  337. 

Fire  engine  pump,  97. 

Firth  of  Forth  Bridge,  176. 

Flatiron,  electric,  332. 

Fleming's  rule,  319. 

Floating  bodies,  60. 

Fluids,  77. 

Flute,  400. 

Flux,  magnetic,  243,  359. 

Flywheel,  157. 

Foci,  conjugate,  for  lens,  439 ;  for 
mirror,  421. 

Focus,  of  lens,  438;  of  mirror,  417; 
real,  420  ;  virtual,  419. 

Fog,  214. 

Foot,  4 ;  -candle,  413  ;   -pound,  28. 

Force,  buoyant,  59  ;  centripetal,  148  ; 
of  expansion,  175,  201 ;  of  friction, 
42;  lines  of,  242;  moment  of,  17; 
vs.  pressure,  51 ;  unbalanced,  149 ; 
unit  of,  7,  155 ;  useful  component 
of,  111. 

Force  pump,  96. 

Forces,  composition  of,  108 ;  equili- 
brant  of,  107  ;  molecular,  73  ;  non- 
parallel,  105  ;  parallel,  25  ;  parallelo- 
gram of,  106  ;  represented  by  arrows, 
105  ;  resolution  of,  109  ;  resultant  of, 
106. 

Franklin,  205,  253,  260. 

Fraunhofer  lines,  458;  meaning  of, 
461. 


482 


INDEX 


Freezing,    by    boiling,    215 ;     evolves 

heat,    203;     -point,    172,    199,    200 

(table). 
Frequency,  of  alternating  current,  365  ; 

of  sound  waves,  382  ;  of  water  waves, 

379. 
Friction,  40  ;  on  incline,  116;  produces 

electricity,  248  ;  produces  heat,  170  ; 

in  water  pipes,  69. 
Frost,  214. 

Fulcrum,  14 ;  force  at,  17. 
Fundamental,  of  string,  391 ;  units,  11. 
Furnace,  188. 
Fuses,  332. 

Galileo,  86,  141. 

Galvani,  263. 

Galvanometers,  281. 

Gas,  engine,  230;  formula,  183; 
standards  for,  409 ;  thermometer, 
181. 

Gases,  properties  of,  see  Air. 

Gauge,  Bourdon,  69,  92 ;  mercury,  68, 
92  ;  steam,  222  ;  water,  56,  222. 

Gay-Lussac,  181. 

Geissler  tube,  476. 

Generator,  318,  321  to  329;  A.C.,  322, 
363  to  367  ;  compound,  328  ;  multi- 
polar,  326;  series,  328;  shunt,  328. 

Gilbert,  241. 

Girder,  115,  130. 

Grade,  32. 

Gram,  weight,  7 ;  mass,  154. 

Gramme  ring,  323,  370. 

Gravity,  acceleration  of,  142  ;  cell,  269  ; 
center  of,  20  ;  specific,  62. 

Guericke,  Otto  von,  82,  86. 

Guitar,  399. 

Hall-time  shaft,  232. 

Heat,  conduction  of,  189 ;  convection 
of,  186 ;  generated  by  electric  cur- 
rent, 333  ;  latent,  202,  209  ;  mechani- 
cal equivalent  of,  234 ;  molecular 
theory  of,  192 ;  radiation  of,  191  • 
sources  of,  170;  specific,  197; 
units  of,  196. 

Heater,  for  hot  water,  187. 

Heating,  electric,  332;  hot  air,  188; 
hot  water,  187 ;  indirect,  189. 

Hefner,  409. 


Helmholtz,  387,  389;   resonator,  391. 
Henry,    Joseph,    electromagnet,    275, 

318 ;    study  of  spark,  469. 
Hertz,  467,  471. 
Hooke's  law,  123. 
Horse  power,  37. 
Horse-power  hour,  330. 
Hot-air,  engine,  185 ;  furnace,  188. 
Humidity,  212. 
Huygens,  461. 
Hydraulic,  elevator,  50 ;  machines,  47 ; 

press,  48. 
Hydraulic  analogue,  of  condenser,  258 ; 

of  current,  266 ;   of  voltmeter,  288. 
Hydrometer,  65. 
Hydrostatic  bellows,  50. 
Hygrometer,  217. 

Ice,  artificial,  216. 

Ignition,  312. 

Illumination,  405. 

Image,     construction     of,    lens,    440, 

mirror,      420 ;       defects     of,      442 ; 

formed     by    lens,    440,     by     plane 

mirror,  415,  by  pinhole,  406  ;   size  of, 

lens,  441,  mirror,  421;  virtual,  420. 
Impulse,  165. 
Incandescent  lamp,  337 ;    vacuum  in, 

83. 

Incidence,  angle  of,  415,  429. 
Inclined  plane,  31,  116. 
Index  of  refraction,  429,  433,  434. 
Induced,    current,    309;    e.  m.  f.,  319; 

magnetism,  244. 

Induction,  electric,  255  ;  magnetic,  244. 
Induction  coil,  310. 
Induction  motor,  368. 
Inertia,   146,  312;    in  curved  motion, 

148. 

Infra-red,  466. 

Insulators,  electric,  249 ;  heat,  189. 
Interaction,  152. 
Interference,  of  light,  465 ;    of  sound.. 

394. 

Ions,  266. 
Isobars,  91. 

Jackscrew,  33. 

Joule,  161,  331. 

Joule,  James  Prescott,  234. 

Jump-spark  ignition,  311. 


INDEX 


483 


Kelvin,  469. 

Key,  telegraphic,  277. 

Kilogram,  mass,  154 ;  weight,  7. 

Kilowatt,  330. 

Kilowatt  hour,  330. 

Kinetic  energy,  157. 

Kinetic  theory,  102. 

Kirchhoff,  459. 

Koenig's  manometric  flame,  392. 

Lactometer,  65. 

Laminated  core,  362. 

Lamps,  illuminating  power  of,  408 ; 
kinds  of,  334  to  339. 

Lantern,  projecting,  444. 

Latent  heat,  ice  to  water,  202 ;  water 
to  steam,  209. 

Left-hand  rule,  341. 

Length,  units  of,  4. 

Lens,  achromatic,  457  ;  camera,  443  ; 
converging,  437  to  441 ;  crystalline, 
445 ;  cylindrical,  447 ;  diverging, 
438,  441 ;  focal  length  of,  438 ;  for- 
mula, 439  ;  images  formed  by,  440  ; 
magnifying  power  of,  448. 

Levers,  13  to  21. 

Leyden  jar,  257  ;  discharge  of,  469. 

Lifting  effect,  of  air,  94;  of  water, 
59. 

Light,  analysis  of,  456 ;  color  of,  456 
to  467 ;  electric,  334 ;  electromag- 
netic theory  of,  467 ;  illumination 
by,  405  to  413  ;  interference  of,  465  ; 
nature  of,  461 ;  reflection  of,  414  to 
424;  refraction  of,  427  to  442; 
speed  of,  431 ;  wave  length  of,  462. 

Lightning,  253. 

Lines  of  force,  242. 

Liquids,  buoyant  effect  in,  58  to  61 ; 
compressibility  of,  78 ;  conduction 
of  electricity  by,  340  ;  conduction  of 
heat  by,  190  ;  in  connected  vessels, 
55 ;  expansion  of,  178 ;  molecular 
attractions  in,  78  ;  pressure  in,  52  to 
57 ;  pressure  transmitted  by,  47  to 
51 ;  sound  transmitted  by,  375. 

Liter,  6. 

Local  action  in  cell,  268. 

Local  battery  system,  315. 

Locomotive  boiler,  221. 

Lodestone,  238. 


Longitudinal  vibrations,  381. 
Loudness,  384,  387. 

Machines,  1,  13;  alternating  current, 
358  to  370;  direct  current,  318  to 
329,  340  to  347 ;  electrostatic,  252, 
259;  frictional  electric,  252;  hy- 
draulic, 47  to  51,  70  to  72  ;  induction 
electric,  259;  pneumatic,  77  to  83, 
95  to  99  ;  simple,  13  to  43  ;  talking, 
401,  402  ;  for  testing  materials,  128 ; 
thermal,  185,  219  to  234. 

Magdeburg  hemispheres,  86. 

Magnet,  artificial,  238;  broken,  245; 
current  induced  by,  308 ;  earth  a, 
241;  electro-,  274  to  278,  320; 
electro-,  self-induction  of,  312  ;  field 
around,  242 ;  by  induction,  244 ; 
natural,  238  ;  permanent,  326. 

Magnetic  field,  around  coil,  273 ; 
around  current,  272  ;  around  magnet, 
242  ;  of  generator,  321 ;  rotating,  368  ; 
side  push  of,  340 ;  wire  cutting,  319. 

Magnetic  poles,  239. 

Magnetism,  238  to  247  ;  induced,  244  ; 
molecular  theory  of,  246 ;  residual, 
274. 

Magnetite,  238. 

Magneto,  327. 

Magnifying  glass,  448. 

Magnifying  power,  of  binocular,  453 ; 
of  lens,  448 ;  of  microscope,  450 ;  of 
opera  glass,  452 ;  of  telescope,  451. 

Major,  scale,  396 ;  triad,  396. 

Make-and-break  ignition,  312. 

Mandolin,  399. 

Manometer,  68,  91. 

Manometric  flame,  392. 

Marconi,  472. 

Mariotte,  80. 

Mass,  154. 

Maxwell,  467. 

Mayer,  165. 

Mechanical  advantage,  25. 

Mechanical  equivalent  of  heat,  234. 

Mechanics,  Chapters  II  to  IX,  see 
table  of  contents. 

Medical  coil,  311. 

Megaphone,  385. 

Melting  point,  199,  200  (table),  effect 
of  pressure  on,  201. 


484 


INDEX 


Metallized  filament,  338. 

Meter,  4  ;  water-,  70. 

Mho,  294. 

Micrometer  screw,  35. 

Microphone,  314,  472. 

Microscope,  449  ;  use  of  mirror  in,  419. 

Mil-foot,  298. 

Milk,  testing  of,  65. 

Mirror,  concave,  417 ;  convex,  419 ; 
focus  of,  417,  418;  formula,  423; 
parabolic,  418 ;  plane,  415. 

Mixtures,  method  of,  198. 

Moisture,  in  atmosphere,  211. 

Molecular  forces,  73. 

Molecular  theory,  of  gases,  102;  of 
heat,  192  ;  of  magnetism,  245. 

Moments,  principle  of,  17. 

Momentum,  165  ;  equation,  166 ;  units 
of,  167. 

Moon,  attracts  earth,  154 ;  eclipse  of, 
407. 

Morse,  276. 

Motion,  laws  of,  133  to  143. 

Motor,  alternating  current,  368 ; 
commutator,  368 ;  efficiency,  346 ; 
electric,  340;  forms  of,  342;  in- 
duction, 368  ;  rule,  341 ;  series,  344  ; 
shunt,  344;  starting  a,  343;  syn- 
chronous, 368;  water,  71. 

Moving  pictures,  445. 

Musical,  instruments,  397  to  400; 
scale,  396;  sounds,  386. 

Neutral  layer,  130. 

Newcomen,  219. 

Newton,   corpuscular  theory  of  light, 

461 ;   laws  of  mechanics,  146. 
Nodes,  379. 
Noise,  386. 


Octave,  396. 

Oersted,  271. 

Ohm,  286. 

Ohm's  law,  289. 

Onnes,  185. 

Opera  glass,  452. 

Optical  instruments,  416,  419,  443  to 

453,  458. 
Organ  pipe,  399. 
Oscillations  of  spark,  469. 


Overtones,  391. 
Ozone,  254. 

Parallel,  circuits,  293 ;  forces,  25. 

Parallelogram  of  forces,  106. 

Parsons  turbine,  229. 

Pascal,  experiments  with  barometer, 
88  ;  principle,  48  ;  vases,  53. 

Pelton  wheel,  71. 

Pendulum,  142, 177  ;  resonance  of,  470. 

Penumbra,  407. 

Period,  380. 

Permeability,  245. 

Perpetual  motion,  165. 

Phase,  of  alternating  current,  365 ;  of 
wave,  379. 

Phonograph,  401. 

Photometer,  409. 

Physics,  description  of,  1 ;  divisions 
of,  2. 

Piano,  397. 

Pigments,  463. 

Pitch,  international,  397 ;  of  screw,  34  ; 
of  sound,  387. 

Plato,  3. 

Pneumatic  machines,  77. 

Polarization,  in  cell,  268. 

Poles,  of  magnet,  238. 

Polyphase  circuit,  365. 

Potential,  difference  of,  267. 

Potential  energy,  162. 

Pound,  mass,  154 ;  weight,  7. 

Power,  37;  alternating  current,  370; 
electric,  329 ;  electrical  transmission 
of  361 ;  factor,  371 ;  horse,  37;  me- 
chanical transmission  of,  38. 

Precipitation,  215. 

Pressure,  of  atmosphere,  85 ;  coeffi- 
cient of,  gases,  181 ;  cooker,  206 ; 
effect  of,  on  boiling,  205 ;  effect  of, 
on  freezing,  201 ;  vs.  force,  51 ;  in 
heavy  liquid,  52  ;  vapor,  205. 

Prism,  435,  436 ;  colors  formed  by,  456. 

Projecting  lantern,  444. 

Pulley,  24,  25,  29 ;  differential,  30. 

Pumps,  95  to  98. 

Quality,  of  sound,  388. 

Radiation,  191. 
Radio-activity,  478. 


INDEX 


485 


Radium,  478. 

Rain,  214. 

Rays,  cathode,  476;  infra-red  and 
ultra-violet,  466;  light,  415,  432; 
Roentgen,  477. 

Reaction,  154. 

Receiver,  telephone,  313. 

Refining  metals,  351. 

Reflection,  diffused,  414;  law  of,  415; 
of  light,  414  to  424  ;  of  sound,  385  ; 
total,  434. 

Refraction,  by  atmosphere,  430;  ex- 
planation of,  433;  in  glass,  429; 
index  of,  433  ;  law  of,  428  ;  in  plate, 
436 ;  in  prism,  436 ;  in  water,  427. 

Regnault,  182. 

Relay,  telegraphic,  278. 

Resistance,  258,  267  ;  box,  301 ;  compu- 
tation of,  297  ;  internal  and  external, 
286 ;  measurement  of,  302  ;  specific 
(with  values),  298;  unit  of,  286. 

Resolution  of  forces,  109. 

Resonance,  acoustical,  390;  electrical, 
470  ;  of  pendulums,  470. 

Resultant,  106. 

Retina,  446. 

Rheostat,  300. 

Right-hand  rule,  319. 

Rivet,  121. 

Roentgen  rays,  477. 

Roller  bearings,  43. 

Rolling  friction,  42. 

Roof  truss,  112. 

Rotating  field,  368. 

Rowland,  235. 

Ruhmkorff  coil,  311. 

Safety  valve,  223. 

Sail  boat,  115. 

Sal-ammoniac  cell,  270. 

Scale,  musical,  396. 

Screw,  33. 

Self-induction,  312. 

Self-lighting  mantle,  101. 

Series,  circuits,  292;    generator,  328; 

motor,  344. 
Sextant,  416. 
Shadow,  407. 
Shear,  121. 
Shunt,  circuits,  293 ;    generator,  328 ; 

motor,  344. 


Sighting,  451. 

Siphon,  98. 

Siren,  388. 

Snow,  214. 

Solids,  conductivity,  electrical,  298; 
thermal,  189;  density  of,  9;  ex- 
pansion of,  174 ;  sound  transmitted 
by,  375 ;  specific  gravity  of,  62. 

Solutions,  conduction  by,  348. 

Sonometer,  398. 

Sound,  374  to  404 ;  intensity  of,  384, 
387 ;  interference  of,  394 ;  nature 
of,  378,  382  ;  reflection  of,  385 ;  sen- 
sation of,  378  ;  velocity  of,  376. 

Sounder,  telegraphic,  277. 

Sounding  board,  398. 

Spark,  oscillations  of,  469. 

Sparking  voltage,  475. 

Speaking  tubes,  385. 

Specific,  gravity,  62  to  66 ;  heat,  197, 
198  (table). 

Spectroscope,  457. 

Spectrum,  456;  absorption,  459; 
bright  line,  459 ;  continuous,  459 : 
solar,  458. 

Spectrum  analysis,  459. 

Speed,  133  (table);  of  electric  waves, 
471 ;  of  light,  431 ;  of  light  in  water, 
434  ;  of  sound,  376. 

Spyglass,  451. 

Squirrel-cage  rotor,  370. 

Standard,  lamp,  409  ;   weight,  155. 

Steam,  engine,  219 ;  latent  heat  of, 
209 ;  turbine,  227. 

Stereopticon,  444. 

Stiffness  of  beams,  128. 

Storage  battery,  352. 

Strain,  122. 

Street-car  motor,  345. 

Strength,  of  beams,  129  ;  breaking,  124. 

Stress,  122. 

Strings,  vibrating,  391,  398. 

Submarine  telegraph,  278. 

Suction  pump,  95. 

Surveyor's  level,  452. 

Tables,  accelerations,  136 ;  accelera- 
tion units,  135  ;  boiling  points,  207  ; 
coefficients  of  expansion,  176 ;  den- 
sities, 9  ;  "  efficiency  "  of  electric 
lamps,  339 ;  electrical  conductors 


486 


INDEX 


and  insulators,  249  ;  electrical  units, 
287 ;  electrochemical  equivalents, 
351 ;  force  units,  151 ;  heat  distri- 
bution in  engines,  234  ;  of  intervals 
in  musical  scale,  397 ;  length  units, 
4 ;  melting  points,  200  ;  moisture  in 
air,  211;  momentum  units,  167; 
specific  heats,  198 ;  specific  resist- 
ance, 298  (in  text)  ;  speeds,  133 ; 
volume  units,  6 ;  wave  length  of 
light,  462 ;  weight  units,  7 ;  wire 
(gauge,  diameter,  area,  carrying 
capacity),  304;  work  units,  160. 

Tantalum  lamp,  338. 

Telegraph,  276 ;  wireless,  472. 

Telephone,  313  ;  wireless,  474. 

Telescope,  astronomical,  450 ;  erect- 
ing, 451 ;  reflecting,  419. 

Temperature,  absolute,  182  ;  low,  185  ; 
regulator,  175. 

Tensile  strength,  127. 

Tension,  121,  123  ;  vapor,  205. 

Tension  members,  114. 

Terminal  voltage,  291. 

Thermometer,  Centigrade,  172;  clini- 
cal, 173  ;  Fahrenheit,  172  ;  gas,  181 ; 
maximum,  173 ;  mercury,  171 ; 
minimum,  173 ;  wet  and  dry  bulb, 
212. 

Thermos  bottle,  191. 

Thomson,  477. 

Thumb  rule,  for  coil,  274 ;  for  wire, 
272. 

Toepler-Holtz  machine,  259. 

Torque,  344. 

Torricelli,  87. 

Transformer,  358. 

Transmitter,  telephone,  314. 

Transverse  vibrations,  380. 

Triad,  major,  396. 

Trombone,  400. 

Truss,  roof,  112. 

Tungsten  lamp,  338. 

Tuning  fork,  374. 

Turbine,  Curtis,  228;  Parsons,  229; 
steam,  227 ;  water,  72. 

Twisting,  121,  123. 

Tyndall,  197. 

Ultra-violet  light,  466. 
Umbra,  407. 


Units,  3;  of  acceleration,  235;  oi 
area,  5;  of  current,  281,  283;  of 
density,  9  ;  electrical,  287  ;  of  elec- 
trical power,  329,  347 ;  of  electrical 
work,  330,  331 ;  of  electromotive 
force,  286 ;  of  force,  151 ;  funda- 
mental, 11;  of  heat,  196,  235;  of 
illumination,  413  ;  of  kinetic  energy, 


160 
409 
167 


of  length,  4  ;   of  light  intensity, 
of  mass,  154 ;    of  momentum, 


of  power,  38,  329,  347;  of 
pressure,  51 ;  of  resistance,  286,  298  ; 
of  speed  or  velocity,  133  ;  of  volume, 
6 ;  of  weight,  7 ;  of  work,  28,  235, 
330,  331. 
Unit  stress  and  strain,  125. 

Vacuum,  bottle,  191  ;  cleaner,  83 ; 
discharge  in,  475 ;  gauge,  92 ;  pan, 
206 ;  pumps,  81 ;  sound  not  carried 
by,  375. 

Vapor  pressure,  205. 

Velocity,  of  light,  431 ;  of  molecules, 
102  ;  of  sound,  376. 

Ventilation,  188. 

Vibration,  made  visible,  375 ;  sym- 
pathetic, 389. 

Violin,  399. 

Virtual  image,  lens,  441 ;  mirror,  420. 

Visual  angle,  447. 

Voice,  400. 

Volt,  286. 

Volta,  263. 

Voltage,  sparking,  475;  terminal,  291. 

Voltmeter,  287. 

Watch,  balance  wheel,  177 ;  stop-,  12. 
Water,    density   of,    179;     gauge,    56; 

meter,  70  ;   motor,  71 ;   turbine,  72  ; 

waves,  378 ;   wheels,  71 ;   works,  67, 
Watt,  329,  347. 
Watt,  James,  horse  power,  37 ;    steam 

engine,  220. 
Wattmeter,  371. 
Wave,    front,    432;    length    of   light, 

462 ;   model,    381 ;    theory   of  light, 

461. 
Waves,  electric,  469,  471 ;    light,  432 ; 

longitudinal,  381 ;  sound,  382  ;  trans- 
verse, 380 ;  water,  378. 
Weather  map,  90. 


INDEX 


487 


Wedge,  33. 

Weight,  of  air,  84 ;   standard  and  local, 

155  ;  units  of,  7. 
Welding,  electric,  360. 
Wheatstone  bridge,  302. 
Wheel  and  axle,  22. 
Wind  instruments,  399. 
Wireless,  telegraphy,  472 ;   telephony, 

474. 
Wire  table,  304. 


Work,  definition  of,  28  ;  electrical,  330  ; 
and  energy,  157;  and  power,  37; 
principle  of,  29  ;  units  of,  28,  235 
330,  331. 

X-rays,  477. 

X-ray  tube,  vacuum  in,  83. 

Young,  462. 

Zero,  absolute,  183. 


Printed  in  the  United  States  of  America. 


Date  Due 


NOV  7 


1930 


NOV  21 
9 


1930 


1942 


1930 


yj 


j*ni 


-CCT- 


1932 


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~^4~ 


1936 


311 


jaa 


SEP 


LIBRARY 

COLLEGE    OF    DENTISTRY 
UNIVERSITY    OF  CALIFORNIA 


